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Full text of "Cotton spinning calculations and yarn costs : a practical and comprehensive manual of calculations, yarn costs, and other data involved in adapting the machinery in all sections, and for all grades, of spinning and doubling"

h^ A'\''! r'i.' mije ^. p. ^iU pbrarg ^ortl} Olarolina ^tats CHolIegs '"°"f,,M«0UN4 STATE SOI 196507 T - Date Due rk?n-2\:,^a'A2^h i nOMn'ARF FEB 9;-ia66-^ / 1 ' 5N'26 ,*' iT?t./nu •< MftSl ian3 34 ' \-^%s 8 Dec 3 4 DEC ^ 3 W99 i37 l6Feb^ 3^ 22F6b39 IM^: 1 _2ftlVlr!4fl K I : i 8.?/^ Digitized by tine Internet Archive in 2010 with funding from NCSU Libraries http://www.archive.org/details/cottonspinningcaOOwint COTTON SPINNING CALCULATIONS AND YARN COSTS COTTON WEAVING AND DESIGNING. By John T. Taylor, late Lecturer on Cotton Weaving and Designing in the Preston and other Technical Schools. Revised under the direction of F. Wilkinson, Director of the Textile and Engineering School, Bolton. With 402 Diagrams, Crown Svo, "js. 6d, net. THE ELEMENTS OF COTTON SPINNING. By John Morris and F. Wilkinson. With a Preface by Sir B. A. Dodson, C.E., M.I.M.E. With 169 Diagrams and Illustrations. Crown 8vo, "js. 6d. PRINCIPLES OF WORSTED SPINNING. By Howard Priestman. With 118 Illustrations. Svo, 7^. 6d. net. WILD AND CULTIVATED COTTON = PLANTS OF THE WORLD : a Revision of the Genus Gossypium, framed primarily with the object of aiding Planters and Investigators \\ ho may contemplate the Systematic Improve- ment of the Cotton Staple. By Sir George Watt, C.I.E., M.B„ CM., LL.D. (Abd. and Glasg.), F.L.S., formerly Professor of Botany, Calcutta University, and Reporter on Economic Products to the Government of India. With 53 Plates, 9 of which are Coloured. Royal Svo, 30i". net. JACQUARD WEAVING AND DESIGNING. By F. T. Belt., Medallist in Honours and Certificated Teacher in " Linen Manufacturing" and in "Weaving and Pattern Designing," City and Guilds of London Institute. ^^'ith 199 Diagrams. Svo, 12^. net. LONGMANS, GREEN, AND CO. LONDON, NEW YORK, BOMKAY, AND CALCUTTA COTTON SPINNING CALCULATIONS AND YARN COSTS A PRACTICAL AND COMPREHENSIVE MANUAL OF CALCULATIONS, YARN COSTS, AND OTHER DATA IN\'OLVED IN ADAPTING THE MACHINERY IN ALL SECTIONS, AND FOR ALL GRADES, OF SPINNING AND DOUBLING JAMES WINTERBOTTOM LECTURER IN COTTON SPINNING, MUNICIPAL SCHOOL OF TECHNOLOGY, MANCHESTER LONGMANS, GREEN, AND CO. 39 PATERNOSTER ROW, LONDON NEW YORK, BOMBAY, AND CALCUTTA 1907 All rights reserved PREFACE The aim of the author of this work has been to provide the student with particulars of the gearing in all the machines involved in Cotton Spinning, together with a method of calcu- lating the trains of gearing. These are accompanied by suitable examples and exercises. Existing works containing Spinning Calculations appear to deal with this subject in a manner too abstract for the average student. In this book the details connected with the calcu- lations and essential in changing the conditions of working, are fully given. The effects of twist in yarn are introduced in consideration of its importance and in the hope of stimulating further investi- gation of its working. The yarn costs are dealt with particularly to assist students preparing for the City and Guilds of London Institute examina- tions in Cotton Spinning. MANCHESTER, ^^,^ ^ \ ) ' Aurjust, 1907. \ J \ ^^ UBRABY 01? K. Ci STATE COIiliB^MB S5I5 CONTENTS TRANSMISSION OF MOTION PAGE Ascertaining the rate— Direction — Sizes — Effects of changes — Examples and exercises 1 — 15 COTTON MIXING Bale-breakers or cotton pullers and distributors — Their object — Types — Actions — Capacities — S^ieeds — Drafts — Merits and demerits — Examples and exercises — Notes on the stack and direct niethods .... 15 — 25 OPENING AND SCUTCHING Openers — Gearing — Speeds— Methods of feeding — Drafts — Lap weight — Ex- amples and exercises — Scutchers — The gearing — Speeds — Drafts — Lap weight— Production — Lap length motions — Changes in speed, weight, and cotton — Examples and exercises — Positive, semi-, and non-positive draft connections — Non-stop working — Controlling factors— Speed of beaters and fans — Sizes of feed rollers — Overscutching and other defec- tive treatment 25 — 56 CAEDING Cards— The gearing— Speeds— Drafts— Alterations— Functions of parts- Conditions controlling efficiency — Rate of movement of flats — Wrapping — Names applied to cotton in the processes — Counting cotton — Card clothing, counting, preparation for mounting, character of its points — Examples and exercises 56 — 76 PREPARATION FOR, AND COMBING Sliver lap machine — Object — Names and functions of parts — Gearing — Speeds — Drafts — Production — Examples and exercises .... 76 — 80 Ribbon lap machine — Object — Names and functions of parts — Gearing — Speeds — Drafts — Production — Examples and exercises .... 80 — 84 VUl CONTENTS PAGE Combing — Alternative preparation of laps — Objects of combing — The Nasmith comber — Speeds — Drafts, and the limitations in range — Weights of sliver and waste — Examples and exercises 84 — 95 The Heilmann comber — Differences of the duplex and Nasmith^ — Speeds — Drafts — Attaching, how adjusted — Draft restrictions — Items controlling the efficiency — Examples and exercises 95 — 102 ATTENUATING AND EQUALIZING (THE DRAWING PROCESS) The draw-frame — Objects — Number of heads useful — -Object and mode of testing slivers — System of " putting up " — Allocating the drafts — Spacing the sliver — Speeds, drafts, counts and production — Suitable sizes of rollers — Analysis of systems of roller gearing — The arrangement of heads — A mode of ascertaining the total draft — Examples and exercises 102 — 110 ATTENUATING (THE FLY-FRAME PROCESSES) The objects of the fly frames : slubber, intermediate, rover and jack — The necessity for repetition— The object of twisting — The direction of twist- ing, its influence — Twist constants — The gearing in these frames — The names and functions of parts — Effects of altering the cone train — Changes in speed, draft, count, twist and spacing — Examples and exercises — Cone drums and differentials — Reasons for a differential train of fixed value 110—141 Analysis of the action of drawing rollers with deductions .... 152 — 154 SPECIFICATION OF CONDITIONS IN CARDING DEPARTMENT Suitable counts and spindle speeds — "Preparation" defined — Counts practi- cable with the available machinery — Factors controlling the allocation of the total draft — Examples and exercises — Hank indicators 141—152, 154—156 Full bobbin measuring motions 156 SPINNING The mule — Description and functions of parts — Twist constants — Factors controlling the value of all trains — Examples of speeds, twist, draft, count, builder, gain and production— Gearing in mules by Dobson and Barlow, Hetherington, Piatt, Trelfall — Jacking, slow roller, double speed, twisting, hastening, backing-off and taking-up and other motions — Comparison of actual speeds and productions with calculated — Losses in driving — Use of the tachometer and tachoscope — Hank and other indicators — Tables of productions 156 — 204 CONTENTS IX PAGE The ring frame — Geariug — Speeds— Draft— Twist and other changes— Examples and exercises — Comparison of calculated with actual speeds and productions— Losses in driving — Table of productions— Conditions favourable to ring spinning— The influence of twist on the output 204—213 YARNS Twist standards for single— Effects of twist in single— Relative breaking resistance in single 214 216 Twist standards for various kinds of folded yarns— The influence of the direction and extent of twist in the singles upon the strength and other features of the folded yarn— The aims of doubling— Equilibrium in folded yarns— Features developed in folding— To ascertain the suitable twist 216—224 DOUBLING The ring doubling frame— Gearing— Speeds— Twist-production— Examples and exercises— The twiner mule— Gearing — Speeds— Twist-production — Examples and exercises 224 — 230 Winding— Keeling 247—249 COSTS OF YARN Total and details of expenses— Examples of costing— Comparison of cost- Yarn from single and double roving — Combed qualities — Ring yarn — Cotton and yarn price lists — Cost of power space— Power required- Extra cost of combing — Departmental costs 231 — 247 INDEX 251 COTTON SPINNING CALCULATIONS AND COSTS OF YARN Tkansmissiox of Motion The Method of calculating the Rate of Motion, when Tooth Gear is employed. — When wheels are employed in a simple or direct train, as in Fig. 1, their move- ment, in teeth or circumferen- tially, is alike. Their axial movement differs only when the wheels are not alike in size. This difference is, rela- tively, inverse to their teeth pj^ j contents. This is proved by assuming that the wheels A, B, C, and D in Fig. 1 contain 100, 75, 50, and 25 teeth, respectively, and that the first mentioned moves one revolution. Thus, the wheel A moves to the extent of 100 teeth, and since its teeth gear with those of B, and the latter with C, and these also with D, then each of them will move tooth per tooth of A, and therefore each will move 100 teeth. Hence, their respective axial movements will be— A = lor};}|l B = WorU C = JgOf or 2 D = ^Si or 4 The preceding results show that the axial movement or revo- lutions of wheels, under such conditions, are inversely pro- portional to their relative teeth contents, and therefore as follows : — B fiSOmCTY UBRARY mr r Qf^ffi C COTTON SPINNING CALCULATIONS Tooth contents. Ratios of their revolutions. A B 100 75 1 n or 75 100 A C 100 50 1 2 or 50 100 A D 100 25 1 4 or 25 100 B C 75 50 1 n or 50 75 B D 75 25 1 3 or 25 75 C D 50 25 1 2 or 25 50 The Direction of the Movement of Tooth Wheels. — In simple direct trains of wheels this is always respectively alternate. This is seen on reference to Fig. 1. By numbering the wheels in their respective numerical order, it is seen that those having odd numbers will all rotate in the same direction, and reverse to those having even numbers. The following are examples in the application of the afore- mentioned points in respect of Fig. 1 : — Example I. — Assuming A revolves 100 times per minute, at what rates would B, C, and D rotate in that time ? Example II. — Assuming B revolves at the rate of 100 per minute, give the rates of A, C, and D in that time. ■ Example III.— Assuming C makes 100 revolutions, how many would A, B, and D make ? Example IV. — If D made 100 revolutions, how many would A, B, and C make? Answers — Example I. — The movement of A expressed in teeth per minute would be Eevolutions of wheel x number of teeth it contains, this = 100 x 100, which AND COSTS OF YARN 3 number of teeth B, C, and D must likewise move, and therefore the number of teeth moved, per minute, by B divided by the number of teeth which it contains, will give its revolutions in that time. .*. =v = 133^ revolutions per minute of B Similarly — The revolutions per minute of C = ^^ = 200 _- 100 X 100 ._- » » D = 25 ^ Example II. — The number of teeth which B moves per minute = 100 revolutions x 75 teeth, and this number A, C, and D must consequently move, and therefore — The revolutions per minute of A = — ^-tctt — = 75 Example III. — The number of teeth which C moves are 100 x 50, which number A, B, and D must also move, and therefore — rvu ^ r f ^ 1^0 X 50 _ The revolutions or A = — r^^^ — = oO „ „ D = 15^° = 200 Example IV. — The number of teeth moved by D are 100 x 25, and therefore A, B, and C will move a like number ; therefore— The revolutions of A = — , ... " = 25 100 X 25 _ 1 100 X 25 _ . ^ - ~50 Tlie Relative Rates of Rotation of the Wheels comprised in any Direct Train are respectively inverse to their Teeth Contents. — This is seen to be the case in all the preceding examples. Thus in — COTTON SPINNING CALCULATIONS Answer to Example I. — A:B: : 100: ; 1331, or as 1 -n A:C: : 100: ;200 !> 1 :2 A:D: : 100: :400 )) 1 :4 Answer to Example II. — B : A: :100; : 75 » n : 1 B:C : :100: ;150 >) 1 ; :li B:D: : 100: 300 » 1 : ;3 Ansiver to Example III. — C :A: :100: : 50 >J 2: : 1 C: B: :100: : 66| J> U: 1 C:D: :100; ;200 V i : 2 Answer to Example IV. — D: A: : 100: :25 )) 4 : : 1 D:B: : 100: ;33i }1 3: 1 D:C: : 100: 50 )1 2: 1 Examples in Respect of the Direction of Rotation. — In Example I. commence by numbering A, 1 ; B, 2 ; C, 3 ; D, 4 ; thus A and C move in the opposite direction to B and D. In Example II. commence by numbering B, 1 ; A, 2 ; C, 2 ; D, 3 ; thus A and C move reverse to B and D, NoTK. — The reason for numbering A and C the same is because that is their relative order. In Example III. commence by numbering C, 1 ; D, 2 ; B, 2 ; A, 3 ; thus C and A move in the opposite direction to D and B, In Example IV. the numbering is D, 1 ; C, 2 ; B, 3 ; A, 4 ; thus D and B move in the opposite direction to C. and A. Direct and Indirect Trains. — When wheels are arranged in an indirect train! (composed of two or more simple trains), as con- tained in Fig. 2, the conditions of transmission differ from those obtaining in direct trains as contained in Fig. 1. The difference in Fig. 2 consists in the wheels B and C being united and have a common axis. These must therefore revolve together. Motion from A to D is imparted to the rim of B by that of A, thence from the rim of B to its hub, and thence to the rim of C, and from this part to the rim of D. The effects of B and C being so coupled are that their Fig. 2. AND COSTS OF YARN 5 movement iu teeth is only alike when they contain the same number of teeth. Their relative movement in teeth differs in the direct ratio of their teeth contents. Thus, if in Fig. 2, A, B, C, D contain 40, 20, 60, and 20 teeth respectively — The revolutions of A will be to those of B j» jj ^ j> 5> -L^ 20 : 40, or as 1 : 2 1 : 1 20 : 60, or as 1 : 3 This shows, in two only of the three instances that the relative rotation is the inverse of their dimensions, and hence the rule, " revolutions of wheels are relatively inverse to their teeth contents," is only applicable in respect of direct trains of wheels. Fig. 2 is an indirect train, and comprises two direct trains of wheels, namely, AB and CD. The effects of their combination may be ascertained by multiplying their separate values, together, thus — 2x3 = 6 or the movement of A : D : : 1 : 6 If A, therefore, made 20 revolutions, the movement of D in revolutions would be 20 X 6 = 120, because A and B would move 20 X 40 teeth, and therefore B and C would make 20 X 40 1 , . r^ ;i T^ n 20 X 40 X 60 , ,, — ^ — revolutions, C and D would move ^7) teeth ; and therefore the revolutions of D would be — ^ ^^ — = 120, ZO X zu or the value of the train multiplied by the revolutions of its first wheel. The following is a summary of the foregoing deductions in respect of — Direct Trains of Wheels. — 1. The circumferential or teeth rate of the movement is alike in all the wheels comprised in a direct train of wheels. 2. The rate of rotation is relatively inverse to the circum- ference or teeth contents of the wheels comprised in a direct train. 6 COTTON SPINNING CALCULATIONS 3. The direction of rotation is alternate at each successive wheel, and when numbered in progressive order, the direction of the odd-numbered wheels will be alike and opposite to those which are even numbered. Indirect Trains of Wheels. — 4. The circumferential or tooth rate of the movement is alike only in those wheels comprised in each of the several direct trains which constitute any indirect train. 5. The rate of rotation is relatively inverse to the tooth contents of those wheels comprised in each only of the several direct trains of which the indirect train is constituted. 6. The direction of rotation is alternate at each successive wheel in any one only of the several direct trains which con- stitute the indirect train. 7. The direction of rotation is alternate throughout an indirect train when those wheels which are fastened to each other, by a shaft or other coupling, are regarded, when numbering, as only one wheel : thus in Fig. 2 the wheels A, B, C, D would be num- bered 1, 2, 2, 3 respectively, so that the direction of B and C would be that opposite to A and D. 8. The circumferential rate as well as the relative rotation, in indirect trains, is ascertained by treating them as so many simple trains as they may comprise. Classification of Wheels. — When the function of a wheel is to convey motion from hub or axle to rim, and therefrom to another wheel, it is termed a driver. When the motion is received at the rim, from another wheel, and passes thence to its hub or a^le, it is designated a driven wheel. When the function of a wheel is merely to convey motion along its rim from wheel to wheel, it is termed a carrier wheel, but when such a wheel has also to transmit movement to its hub or axle, for driving some other part, it would also be termed a driven wheel, but only in respect of the latter connection. Examples in the Classification of wheels in Figs. 1, 2, 3 — Fig. 1, assuming the motion flowing from A to D — A is a driver (motion flowing from the axle to rim). AND COSTS OF YARN 7 B is a carrier (motion flowing merely^along the rim). n ^ )> jj )j >> D is a driven (motion flowing from the rim to the axle). If the motion was from D to A then — D would be a driver. C ,, carrier. B „ „ A ,, driven. Fig. 2, assuming the motion passing from A to D — A would be a driver. B ,, driven (the motion here passes to the axle) C ,, driver (the motion here passes from axle to the rim). D would be driven. If the motion passed from D to A the above functions would be reversed. Fig. 3, assuming the motion passed from A to E, and G — A to E : A would be a driver. B ,, carrier. C ,, driven. D ,, driver. E ,, driven. A to G : A and F are drivers. B and G are driven. Examples in respect of the direction of rotation with the motion as stated above — Fig. 1. — A and C, their numbers respectively being 1 and 3 ; B and D, their numbers even 2 and 4, their direction being opposite to A and C. Fig. 2. — A and D the same direction and positive (since their progressive numbers are, according to the definition, odd numbers positive and even numbers negative) ; B and C being numbered 2, 2, and therefore negative. Fig. 3. — The numerical order of A, C, D, G, is 1, 3, 3, 3 8 COTTON SPINNING CALCULATIONS respectively, and therefore in the positive direction ; B, F, E 2, 2, and 4 respectively, and therefore negative. The Method of calculating the Value of Wheel Trains. — A simple method, applicable in direct or indirect trains, is deduced from the foregoing procedure in ascertaining the relative movements of the wheels in Figs. 1 and 2. The value of the trains, in each of those instances, is found by multiplying the sizes of the driver wheels, in teeth, together for a numerator, and those of the driven wheels together for a denominator — the resultant being the value of the train ; or, the relation of 1 4 2 D E 5 G F r 3 Fig. 3. the final wheel in terms of one of the first wheel. This result, when further multiplied by the revolutions of the first wheel, in a given time, obtains the revolutions of the final wheel in that time. Applying this in finding the revolutions per minute of shafts 2, 3, 4, and 5 respectively, in Fig. 3, when the sizes of the wheels in teeth, alphabetically, are : 40, 20, 50, 25, 100, 40, 80 ; and (1) is assumed to make 500 revolutions per minute, the following are the results : — (1) A is a driver, B a carrier, G is a driven wheel, and therefore — The revolutions per minute of shaft (2) = tJ] X 500 = 400 AND COSTS OF YARN 9 (2) A and D are drivers, B is a carrier, C and E are driven wheels, and hence — Revolutions of shaft (3) per miaute = fg X ,%'^o ^ ^0^ = 100 (3) Here A is a driver aad B the driven wheels, therefore— |}} X 500 = 1000 revolutions of shaft (4) per minute (4) Here A and F are drivers, and B and G are driven wheels, hence — 40 . 40 The revolutions of shaft (5) per minute = ^^ .^^ X 500 = 1333.^ The Effects of changing Wheels. — The effects of changing the size of any wheel depends upon its function. If a driver wheel, the axial rate of all other wheels receiving motion from it will be altered in the direct ratio of the change, because the movement of the new wheel, in teeth, per revolution, will be altered in that ratio ; and this will affect all the others depending upon it for their motion in like terms. Hence, changing A to 30, and taking the revolutions of A at 500 per minute, would cause — The shaft (2) to rotate at — 500 X g^, by gear; or,, by proportion : 400 X f g = 300 per minute The shaft (3) to rotate at — 500 X |§ X y^fpQ, by gear ; or, by proportion : 100 X fg = 75 per minute The shaft (4) to rotate at — 500 X f§, by gear ; or, by proportion : 1000 X |g = 750 per minute The shaft (5) to rotate at — 500 X ?,§ X |§, by gear ; or, by proportion : 13331 X |g = ioOO per minute In case of a driven u-liecl hcing altered, the axial rate of tliose wheels, dependent upon it for their motion, woidd be affected in the 10 COTTON SPINNING CALCULATIONS inverse ratio to that change. — Because the rate of movement of its teeth would be unaltered, because the wheel receives its motion from the same wheel as hitherto. Its axial rate would be increased when the new wheel contains less, and diminished if containing more, teeth. Hence, altering the wheel C to 40 instead of the wheel A, assuming the latter to make 500 revolutions i^er minute, would have the following results : — Shaft (2) would rotate at — 500 X IJ], or 400 X |g = 500 revolutions per minute Shaft (3) would rotate at — 500 X |£- X -i%\ = 125 revolutions per minute Shafts (4) and (5) would not be altered. If B were altered to 30 instead of C, then the following would be the result : — Shaf ts'(2) and (3) would not have their speeds affected, because C would move at the same tooth rate ; thus — Shaft (4) would rotate at — 500 X II], or 1000 X |g = 666§ revolutions per minute Shaft (5) would rotate at — 500 X *{] X If], or 1333^ X |[] = 888| revolutions per minute The foregoing show that increasing the size of a driver wheel increases proportionately the speeds of the subsequent wheels in the train, and vice versa ; that increasing the size of a driven wheel proportionately decreases the speeds of the sub- sequent wheels in the train, and vice versa. Therefore, to determine the teeth contents or size of a wheel when it is required to alter the speeds, the procedure must be as follows : — In the case of driver wheels : the size of the wheel it is decided to alter, multiplied by the speed required, and divided by the existing speed, will give the wheel required, because the size of this wheel must be altered in the direct proportion of the present rate to the required rate. In case of driven wheels : the size of the wheel it is decided to alter, multiplied by the existing speed, and divided by required AND COSTS OF YARN 11 speed, will give the wheel required, because the driven wheel must be altered in the inverse proportion of the present rate to the required rate. To determme the sizes or teeth contents of wheels to employ in a train in order to obtain a specific speed of the final wheel. Ascertain the value of the train required ; the distance of the shafts apart ; the space available for the wheels ; the pitch of the teeth that affords sufficient strength, with due regard to lightness ; the direction of motion. This latter will decide whether the number of wheels to employ should be odd or even. The number of wheels should be as few as possible. The space available restricts their size. The distance apart of the two centres multiplied by 2(3*1416) will give the sum of the circumferences of the wheels required. This divided by the suitable pitch of the teeth gives the sum of their teeth contents, whatever the number of wheels, when they are arranged with their centres in a straight line. If their centres are arranged otherwise, it would be necessary to determine the sum of their distances apart. The latter would control the sum of their teeth contents. The contents of each wheel would then be decided according to the intermediate axial speeds required. Under conditions similar to Fig. 2, where the ratio in the train is 6 to 1 , and the latter has to rotate in the opposite direction to the former, an odd number of wheels must be employed. The following would suffice : A, six times the smallest size of D practicable, and these connected by a suitable carrier, or odd number of carriers. If there is a wide difference in the sizes of the wheels this is impracticable, then A, 2*4 times B ; and C, 2*5 times D should be employed. Exercises. — Ascertain the wheels convenient to secure the undermentionecl values in the following trains : — 1. A direct train to consist of six wheels with axial motion in the ratios of 1, 2, 3, 4, 5, and 6 respectively. 2. A direct train to consist of three wheels with axial motion in the ratios of 1, I, and 3 respectively. 3. An indirect train of six wheels, comprising three direct trains, with the axial ratios 1, 1-6, 3*2, and 8 respectively. 12 COTTON SPINNING CALCULATIONS 4. An indirect train of six wheels, comprising three direct trains with the difference in axial ratios equally distributed, the whole amounting to 8. 5. An indirect train of six wheels, the whole containing a ratio of 1 : 9, one of the direct trains to have the value 2-C8. Rope and Belt Driving. — Eopes and belts are extensively employed in the transmission of motion. The method of calculating the speeds and sizes of the driving surfaces — pulleys and drums — is identical with that in wheel gear, the sizes of the pulleys and drums taking the place of the teeth contents in wheels ; the measurements usual being in inches or feet diameter, these measurements being made from diametrically opposite points of contact of the transmitting medium. Fig. 4. Example 1 (Fig. 4). — At what rates per minute would B, C, D, E, F, and G rotate if the gi'ooved flywheel of the engine A makes 50 revolutions per minute, was 25 feet, and the others 5, 9, 8, 12*5, 5, and 6 feet respectively ? Answers — Eevolutions of B per minute = ;; = 300 5 60 X 25 = 1601 AND COSTS OF YARN 13 Revolutions of D per minute = ^-^= 187'5 _60x25_ " ~ 12-5 ~ _ 60x25 _ " >. - 12-5 -^"^^ p 60 X 25 X 5 ,„„ ^ " = 12^^5^6- = ^^^ The reasons for adopting tliis method of determining the speeds of parts when motion is transmitted by belt or rope gear are as follows : — The circumference of a drum or pulley or a circle when divided by the number 3-1416, gives its diameter; the diameter being easier to measure, it is customary to ascertain the circumference by multiplying the diameter by that number. For practical purposes "/ is considered near enough in this kind of work. The rate of the movement of the strap in calculating is generally assumed to be the same as the contact surface of the drum. This, however, varies con- siderably from that rate, according to the working conditions, such as tension, cohesiveness, and pHability of the belt; distances of the centres apart ; material, sizes, and shape of drums; amount of load. These are not usually recognized in making calculations, but are allowed for in general practice. The rate of the movement of ropes is about the same as the point of contact in well-constructed grooved pulleys. In calculating it is not customary to make an)^ allowance. The rate of movement of the ropes engaging with the grooved flywheel A will therefore be the same as that of the pulley at the centre of the part in con- tact with the rope. If this is 12*5 feet from the centre of the pulley, or equal to 25 feet in diameter, the circumference of such a circle would be 25 feet x 3*1416, and therefore this would be the rate which the rope would move per revolution of A. In 60 revolutions it would, therefore, move the rope 60 times that amount, or — 25' X 3-1416 X 60 The rope moving at this rate about the pulley B, which is 5 feet diameter, or 5' X 3-1416 in circumference, then the number of times which the length repre- senting the circumference is contained in the length of rope passing over the pulley in a given time, will be the rate at which it revolves. Therefore — 25' X 3-1416 X 60 ,, , . , ,• ^ t, onn f7 TTzr-rm — = the rate ot rotation oi 13 = oOO 5 X 3-1416 Since, in rope and belt gearing, drums and pulleys always work in pairs — a driver and driven — and these in calculation are always placed on opposite sides of the equation — when one is the numerator, the other is always the denominator. The necessity for using the constant 3-1416, to convert the diameter into the circumference, occurs just as often a numerator as a denominator, and it always 14 COTTON SPINNING CALCULATIONS cancel?. It is, therefore, left out of the calculation ; hence the rule is as follows : — diameters of drivers revolutions of 1st driver _ ("the revolutions of the last diameters of driven ^ 1 " I driven drum or pulley because— diameters of drivers x revolutions of 1st driver _ ^ diameters of the driven x revolutions of last driven Example 2 (Fig. 4). — Required the revolutions per minute of F, D, C, B, A respectively, when, with the gearing as given in Example 1, G is found to revolve 110 times per minute. Note. — It is best in working questions of this kind to assume the one moving at a known rate the driver. This always simplifies the calculation, whether dealing with rope, belt, or teeth gear. (1) G is a driver and F driven — /, = — = 132 revolutions of F 5 (2) G, E, and A are drivers ; F, A, and D are driven — no X 6 X 12-5 X 25 ^ 206-25 revolutions of D 5 X 25 X 8 (3) G, E, and A are drivers ; F, A, and C are driven— 110 X 6 X 12-5 X 25 ,„„ • , ,. ^ ^ • — _ = 183-3 revolutions of 5 X 25 X 9 (4) G, E, and A are drivers ; F, A, and B are driven— 110 X 6 X 12-5 X 25 ooA ^ I' e-D xxv/_^ /s^ = 330 revolutions of B 5 X 25 X 5 (5) G and E are drivers ; F and A are driven— 110 X 6 X 12-5 5x 25 = G6 revolutions of A Example 3 (Fig. 4).— What sizes of B, C, D, E, and F would be required in order that their revolutions per minute maybe B, 250; C, 214; D, 187 ; E, 150 ; G, 100 respectively, assuming A to make GO revolutions in that time, and to be 25' in diameter ? Here A is the driver, and the rate of the movement of the ropes will be GO X 25' X 31416 per minute. Since B is required to revolve 250 times per minute— 60x25x3-1416 Circumference of B must be = 059 AND COSTS OF YARN 15 A- , F-R 9in,' GO X 25 X 3-1416 or diameter of B x 3-l-il(j = — ^.^ 250 . ,. , .„ GO X 25 X 3-1410 GO x 25 ., /. diameter of B = --r^ q^ttt^— = o-a = ^ 250 X 3-1410 2o0 Diameter of C will be — 60 X 25 _ „, 214 60 X 25 o, and diameter of D 187 and diameter of E = — — ^ = 10' loO In case of F, wliich is also a driver — GO X 25 X diameter of F diameter of E x diameter of G 60 X 25 100 = 100 revolutions of F diameter of E x diameter of G diameter of F . 60 X 25 _ 1 •• 10 X 6 X 100 ~ diameter of F .A- ^ ct:^ 10 X 100 X 6 ., /. diameter of F - — ^^ ^ — = 4 60 X 2o Or, since F and G revolve 150 and 100 respectively, and G is 6 feet in diameter, and it is known that their sizes must be inversely proportional to those rates, then — 6' X 100 ,. , „„ ,, — ^,_- — = diameter of F = 4 150 Bale Breakers or Cotton Pullers. — Fig. 5 is an elevation of the gearing in a well-known make of machine of the Roller type. This type of machine displaced manual pulling, which was previously in vogue, in reducing the cotton to a suitable state of mixing. At present this type of machine is used extensively in old mills which do not make a point of keeping up-to-date. In modern mills a machine known as the Hopper bale breaker, or cotton puller, is found in place of the former, the disadvantages of the roller type of this machine being the dust and noise accompanied by wear and tear and frequent breakages. Its forcible action, creating heavy pressures upon the cotton between edged surfaces, are considered to exercise a 16 COTTON SPINNING CALCULATIONS detrimental effect upon the cotton. There is a great difference in the principle of the two types of machines named. The Hopper has a coarse comhing action, and considerable pressures upon the cotton are eliminated. The productive capacity of a Fig. 5. roller pulling machine ranges up to 100,000 lbs. per 55i hours when worked at the highest pressure. The best results obtainable are when it is run at a high speed for American cotton and at a moderate speed for Egyptian and Indian varieties. The following are the particulars of the parts in the Eoller cotton puller. Fig. 5 : — a, the line shaft making 220 revolutions per minute. h, a drum, 19" in diameter, on the line shaft and driving the machine strap. c, c are swing or *' gallows " pulleys. d represents the fast and loose pulleys on the machine shaft ; these are 16" diameter. e, a grooved rope pulley, 19" diameter, fixed upon the machine shaft, driving a rope which drives the porcupine cylinder. AND COSTS OF YAEN 17 /, a grooved carrier pulley for the above-mentioned rope. g, a grooved pulle}^ lOh" diameter, fixed upon the porcupine shaft and driven b}' the above-mentioned rope. h, a wheel containing 25 teeth, fixed on the machine shaft. i, a wheel on the shaft of the lower second pulling roller, containing 40 teeth, and driven by h. j, a wheel containing 14 teeth, and fixed upon the axis of i. h, a wheel containing 76 teeth, and driven by j. I, a wheel containing 14 teeth, fixed to the axis of k. Ill, a wheel on the lower first pulling roller, containing 76 teeth, and driven by /. n, a wheel fixed on the first pulling roller, containing 17 teeth. 0, a carrier wheel, gearing with ii and j?. }), a wheel on the lattice roller shaft, containing 20 teeth. q, a grooved rope pulley, 10" diameter, attached to e and driving /•. ;•, a grooved pulley, 15" diameter. s, a wheel fixed upon the axis of r, containing 20 teeth. t, a wheel with 60 teeth, fixed on the lattice roller axis ti. h, a wheel with 60 teeth, fixed upon the other vertical lattice shaft and engaged with t. ui and ;/3, wheels on lattice roller shafts, each containing 38 teeth. U2, a carrier wheel, gearing with iii and »3. u, a wheel, 24 teeth, fixed to the lattice roller shaft. V, a carrier wheel engaging with u and ?f. w, X, y, z, wheels containing 24 teeth each, distributing lattice connections. Kevolutions per minute of the various parts in the roller cotton pulling machine (Fig. 5). The machine pulleys r-^ z= 261*25 mi r n ..• n 220x19x25x14x14x17 ,„ The feed lattice roller i6x40^76x7Xx20 = ^ ^ The surface speed in inches per minute = 4*7 X 5*5 x ^^^ = 81"-24 c COTTON SPINNING CALCULATIONS The first pair of pulling rollers — ■p , ,. . , 220X19X25X14X14 _^ iievolutions per mmute = zrp, — 77;^ — W7> — s^ = ^'^^3 ^ 16x40x76x76 c n , 220x19x25x14x14x6x22" ..^„„a Surface speed = -^ — ttt — wt^—^^ ^ =113 -76 ^ 16x40x76x76 7 The second pair of pulling rollers — 13 1 r • * 220X19X25 _., .^ devolutions per mmute = ^^ ,^ = 163'3 ^ 16 X 40 a f 1 . , 220x19x25x6x22 „ Surface speed per mmute = ^^ — ,7^ „ = 3079 ^ ^ lb X 40 7 The porcupine cylinder 220 X nnt.o r^ 16x10 ■D w • ♦ 220x19x21 .^„. Eevolutions per mmute = 1 a^^mT ~ 522-5 2 The lower conveyor lattice rollers — T. , ,. . , 220x19x10x20x60 _ „ _ Eevolutions per minute = -^ — - --- ^^- — „r. = o8'05 ^ 16x15x60x60 Surface rate per minute in inches 58'05 X 5-5 x ---- = 1003"'5 The right-hand elevator lattice roller — 220 X 19 X 10 X 20 16x15x60 = 58-05 Surface rate = 5805 x -~^ = 1003"-5 The left-hand elevator lattice roller- 220x19x10x20x60 16x15x60x60 = 58-05 The first overhead conveyor and distributing roller— .220x19x10x20x34 16 X 15 X 60 X 24 = 58-05 Surface rate = 58-05 X ^^_iiff = 1003"'5 AND COSTS OF YARN 19 The second overhead conveyor and distributing lattice roller — 220 X 19 X 10 X 20 X 24 X 2 4 x 24 _ 10 X 15 X 60 X 24 X 24 x 24 ~ ^'^"^ Surface rate = 58-05 X 5 '5 X '^f- = 1003"-5 All the machines used in connection with cotton spinning contain the power to attenuate the cotton. The term which is most generally used in place of the word attenuation is " draft." The extent of the ''draft" governs the relative weight of the cotton at the different points in the processes. The extent practicable in each machine, and also between the various points in each machine, should be well understood, because it is this which governs the relation in the weight of the cotton in any part of the machine. If a machine, or a part of it, contains a draft of four, the difference in the state of the cotton, as regards its weight, would be four times. This means that it has become four times lighter and longer between the parts referred to. The extent of the draft may be ascertained from the relative rates of the parts moving the cotton, or, from the relation in the weight of the cotton as it passes under the influence of the two points in question. Applying this, in respect of the machine under notice, it is found that the draft between the feed lattice and the first pair of pulling rollers is : (surface movement of the] first pair of pulling rollers! 1.4 ..^ .„ pel* ^i^^^e 1^ i^clies j minute in inches J so that the cotton under the influence of the rollers will be 1*4 times lighter than that upon the lattice, and therefore 1*4 times longer. The following are therefore the drafts between the adjacent parts, in progressive order, in the above-named machine : — 20 COTTON SPINNING CALCULATIONS First and second pair of pulling rollers — 3079 163-3 = 18-85 Second pulling rollers and lower conveyor lattices — 1003-5 "3079- = ^^'^ Lower conveyor and the vertical lattices — 1003-5 1003-5 = 1 Feed lattice and overhead conveyor lattice— 1003-5 _.._ '81-24' - ^^ ^^ Exercise 1. — What would be the speeds, in revolutions per minute, of the under-mentioned parts, if the line-shaft driving drum was 16 inches in diameter instead of 19 inches : (a) the machine pulley ; (&) the feed lattice roller ; (c) the first pair of pulling rollers ; {d) the second pair of pulling rollers ; (e) the porcupiue cylinder ; (/) the lower conveyor lattice roller ; (g) the vertical con- veyor lattice rollers ; {h) the overhead conveyor lattice rollers ? Exercise 2. — What would be the effect upon the speeds of the different parts if the 25 wheel on the machine shaft was changed to 30 after changing the line-shaft drum to 16 inches ? The working of the first of these exercises is as follows : — 220 X 16 ,,,^ (a) — jg— = 220 220 X 25 X 14 X 14 X 17 „ , ,„ ^^ 40 X 76 X 76 X 20 , ,. 4-7 X 16 „„ or, by proportion — ^^ — = 6-'Jb , , 220 X "25 X 14 X 14 , ,^ 5-53 x 16 „ . (c) ACS — 7? HR = 4'66 ; or t^ = 4-6fa ^ ^ 40 X 76 X 7b ly ,,,220x25 ,_. 163-3x61 i^) 40 ^ ' ^^' 19 "^ ,. 2-20 X 21 ,,^ 522-5 x 16 ,,, (^) loi = ^^^ ' '' —IT— = ^^^ ,^, 220 x 10 x 20 X 38 ,.^ 58-05 x 16 ,„ „„ ^^ 15 X 60 X 38 = ^^^ ' '' -^r— = ^^-^^ AND COSTS OF YARN 21 ^,220x10x20 ,_ 58-05x10 ,„q„ ((j) 1-^^-^A = ■iS?; ; or ^7,; = 48-89 15 X 60 19 .,. 220 X 10 X 20 X 24 ,., 58-05 x 16 ,_ ^_ ('0 T r ■ ■ ..^ c. = 48i} ; or ^^^ = 48-89 15 X 60 X 24 Ansioers to Exercise 2 — (a) Machine pulleys, 220. {I) 4-759. (c) 5-57. {d) 165. 19 (p) 440. (/) 48-89. {g) 48-89. Fig. 6 is an elevation of the gearing in a cotton pulling machine of the Hopper type. This type of machine reduces the Fig. g. cotton to a very loose open condition. The advantages of this machine over the roller type of machine are — Greater opening and cleaning power. Less noise and dust when well constructed. Less personal attention. Greater production, about 200,000 lbs. per 55^ hours, without pressure. 22 COTTON SPINNING CALCULATIONS Less risks of fire in this and subsequent machines by its eliminating hard substances. Mixing powers considerable, whereas in the roller type they are very limited. Fewer breakages and up-keep less costly. The machine driving pulleys are on the stripping cylinder shaft, and in the figure they are shown as 12 inches in diameter. These are driven by a strap from a drum on the line shaft, 26 inches in diameter, and making 220 revolutions per minute. (1) Eevolutions per minute of the fast and loose drums of the machine — 220 X 26 12 476| (2) Eevolutions per minute of the supply lattice roller — 220 X 26 X 7 X 24 X 24 X 24 ^ 12 X 20 X 90 X 30 X 30 ~ (3) Eate per minute in feet — 29-36 X 5-5 X 22 T^ ;^ = 42 12 X 7 (4) Eevolutions per minute of the spiked lattice roller — 220 X 26 X 7 J< 24 _ 12 X 20 X 90 ~ (5) Surface rate per minute — 44-49 X 20 X 22 = 233' 12 X 7 (6) Eevolutions per minute of the regulating cylinder- 220 X 26 X 7 X 54 12 X 20 X 90 (7) Surface rate — 100-1 lQQ-1 X 1 4 X 22 _ 12 X T - ^^^ (8) Eevolutions per minute of the stripping cylinder — 220 X 26 , 12 = ^^^^ AND COSTS OF YARN 23 (9) Surface rate — = 1747''5 476|o< 14 X 22 12 X 7 (10) Revolutions per minute of the lower conveyor lattice roller — 220 X 26 X 7 X 8 12 X 18 X 8 (11) Surface rate — 185-37 X 5-5 X 2 2 12 X 7 = 185-37 = 267' (12) Revolutions per minute of the elevating lattice rollers- 220 X 26 X 7 X 6 12 X 18 X 12 = 92-7 (13) Surface rate- 92-7 X 5-5 X 22 _ , W^f ~ ^^^ '^ Exercise 3. — At what rates, in revolutions and feet per minute, would each of the parts in Fig. G rotate if the driving puller's were altered to 15 inches diameter, instead of 12 inches? Exercise 4. — Ascertain the drafts between the different lattices when the conditions are as given in Fig. 6, and also when the machine pulleys are altered to 15 inches ? Exercise 5. — State the effects of changing the 24 wheel, driving the 90, to 20, upon the speed of each part, when the other conditions are as given in Fig. 6. Answers to Exercise 3 — (1) 381-3 revolutions. (8) and (9) 381-3 and 1398 feet. (•2) and (3) 235 and 30-G feet. (10) „ (11) 148-3 „ 213-62,, (4) „ (5) 35-G „ 18G-4 „ (1-2) „ (13) 74-1 „ lOG-8 „ (G) „ (7) 80-0 „ 300-8 „ Ansivei's to Exercise 4 — When the driving pulleys are 12 inches diameter, the draft between feed and spiked lattice is 5-55. When the driving pulleys are 12 inches diameter, the draft between spiked lattice and the lower conveyor lattice is 1-lG. 24 COTTON SPINNING CALCULATIONS "When the driving pulleys are 12 inches diameter, the draft between lower conveyor and elevating lattices is O'o. When the driving pulleys are 15 inches diameter, the speed of all the parts will be decreased in the same proportion, and the drafts will therefore be unaltered. Answers to Exercise 5 — (1) 476^ revolutions. (8) and (9) Unaltered. (2) and (3) 24-46 „ ; 35 feet. (10) „ (11) (4) „ (5) 37 ,. 194 feet. (12) „ (13) (6) „ (7) 83-4 „ 313 3 feet. The usefulness of this machine is infinitely greater than the roller puller. Evidence of this is found in the number of mills which have modified their mixing arrangements since its introduction. The most common practice in using this machine is that of placing the cotton from the various lots of bales in the machine, in the desired proportions, at a rate permitting only of the limited exercise of their opening and mixing functions. When such replaces stack mixing, variations are visible in all the subsequent stages. Extension in the usefulness of the machine is possible by adopting one puller per 30,000 or 40,000 lbs. per week, and adjusting them so that their maximum opening capacities are utilized in that time, the cotton, from the several pullers, supplied with bale cotton in the usual way but in perfect rotation, passing into a common trunk, from which the several exhaust openers draw their supplies. These latter deliver to hopper feeders attached to further openers, fitted with the full width type of beaters. From these the cotton may pass to the scutcher or to the card direct. The hopper feeder to the final opener should be fitted with automatic supply control attached to feed of the opener responsible for its supply. By this system, in a mill consuming 200,000 lbs. of cotton per week, the supply would be drawn from six times the usual number of bales, with the additional advantages that the hard and soft qualities would be unavoidably mixed in the designed proportions con- tinuously. To derive the fullest benefits from the use of the hopper V^^ " ^_ ''^" ^^-^ -a-^^ COLL: AND COSTS OF YAEN 25 cotton puller — as an opening process — it is necessary to bear in mind that the opening, and consequently the cleaning effect, is dependent upon : The rate of movement of the spikes amongst the cotton and the pressure of the cotton against the spiked surfaces; the distance of the points of the spikes on the regulating cylinder from those on the spiked lattice, and the contrasting rates in the movement of these two latter parts. The best speed of the spiked lattice is the highest rate at which it may be worked without undue strain. The rate varies considerably in the various makes, and also with cotton treated. American cotton allows of a higher rate than Indian or Egyptian. The most beneficial speed can be readily ascertained by test. This decided, the regulating cylinder should be adjusted to a point at which the machine produces only the amount of cotton required in the fall working time. Where these items are disregarded the opening and cleaning utility of the machine is only partially realized. The Openee. Fig. 7 contains particulars of the principal parts and their connections in a hopper-fed compound combined opener. Par- ticulars of the other parts and their connections are contained in Figs. 8, 9, 10, and 11. The object of giving the details in five instead of in one figure is to avoid confusion. The speeds of the various parts in Fig. 7 are — Counter shaft 495 revolutions per minute Beater shaft 1028 Cross shaft 21417 Side shaft 428-34 Bottom cone shaft . . . 856'73 ,, Top cone shaft .... 611*95 ,, Porcupine cylinder . . . 440 ,, Fan shaft (1) 1015-4 Fan shaft (2) 1542 26 COTTON SPINNING CALCULATIONS '220 Revs, per min Counter Shaft 16" EXAMILES OF WORKING OUT THE SpEEDS OF THE AcOVE PaKTS. ^•^O X 36 The counter shaft = — ^,7^ = 490 lb The beater ,. = The cross „ = The side ,, = The bottom cone = . The top „ = The porcupine cj'hnder = = 1028 220 X 36 X 27 " 16 X 13 220j^86 ><^27 X 5 _ . 16 X 13 X 24 ~- 220 X 36 X 27 X 5 X 30 103 16 X 13 X 24 X 15 220 X 36 X 27 X 5 X 30 X 40 16 X 13 X 24 X 15 X 20 220 x36: ><27x 5 X 3C 1x40 x5 16 X 13 X 24 X 15 X 20 X 7 220 X 36 X 18 = 856-73 = 61195, say 612 16 X 16 15 557 Fan shaft (1) = 557 x ,;, = 1285 Fan shaft (2) = 1028 x ]} = 1542 AND COSTS OF YARN 27 Exercises kelatikg to Fig. 7. (1) At what speeds would the parts contained in this figure revolve if the line shaft made 250 instead of 220 revolutions per minute ? (2) If the fan-shaft pulley (1) was changed to G inches, at what rate per minute would it revolve ? (3) At what rate per minute would the bottom and top cones revolve if the bottom cone and side-shaft wheels, 20 and 40, were substituted by 24 and 36 respectively ? (4) What size of driving and driven pulleys would alter the rate of the cross shaft from 214-17 to 257 per minute? What effect would such an alteration have upon the speeds of the other parts ? (5) What changes would alter the speed of the beater to 1113 revolutions per minute if the fan and cross shaft are to remain unaltered? (6) At what rates would the top-cone shaft revolve when the cone strap is ■working on the extreme right and left ends respectively ? Answers to Exercises (Fig. 7) — (1) The speed of all the parts would be increased in the same proportion as the change in speeds, thus: 502, 11G8, 243-3, 486-7, 973-5, 684, 500, 1153-8, 1752 respectivelj'. (2) The surface rate of the strap and pulley would be unaltered, and therefore the revolutions per minute would be altered in same proportion as the size of pulley, namely, to 1100. (3) Bottom cone, 458-9 ; top cone, 645. (4) A G-inch driver on the beater shaft, or a 20-inch driven on the cross shaft. The side shaft and bottom and top cones would be altered in the ratio of from 5 to 6, or to 514, 1028, and 734 respectively. (5) The beater pulley to 13 inches ; the pulley driving the cross-shaft pulley 4^*^^ inches, or the cross-shaft pulley 26 inches ; the pulley on fan shaft 6 J inches. (6) 1562 and 352-7 respectively. Calculations relating to the speeds of the parts in Fig. 8. Eevolutions per minute of — m 1 wr n 612 X 4 X 9 X 1 X 12 ^ .^^ The supply lattice roller = 9 x 7 x 7 8^85 — " ^^^ The surface speed in| _ 0-633 X 55 x 22 inches per minute ) 7 ~~ The bottom lattice rollers) ^ 612 x 4 x 23 X 17 X 20 x 20 _ in the hopper J 9 X 55 x 79 X 48 x 48 ~ The surface speed in\ _ 4*25 X 5*5 x 22 _ inches per minute/ 7 —*^^ 28 COTTON SPINNING CALCULATIONS The spiked lattice rollersl ^ 612 x 4 x 23 x 17 _ ^^,^„ in the hopper / 9 X 55 x 79 The surface speed in ) inches per minute/ 24-47 X 5-5 X 22 = 422-98 ■g!i« f)ui|r{iiiiDiu!iiiliiDiia The regulating cylinder = 440 X 6 X 4 X 24 12 X 12 X 48 = 36-6 AND COSTS OF YARN 29 The surface speed in| _ 330 X 18'^ X 2 2 oQr>.;r Qi.i72-8ft inches per minute J 9 7 ~ ' The stripping cylinder = ^^ ~ ^^^ The surface speed inl _ 220 x 16 X 22 _ .. ^ ^^^„ or921-0ft inches per minute J ~ 7 "~ ' Questions relating to Fig. 8. Name the parts affected by each of the followiag alterations, and calculate the effects in revolutions and surface speed in feet per minute : — (7) If the cone strap was successively placed at both extreme pohits on the cone drums. (8) If the pulley on the top-cone shaft was 5 inches diameter instead of 4. ('J) If the pulley on C was changed to 9 inches diameter. (10) If the 80 on the supply lattice roller shaft and the 12 driving it were altered to 84 and 14 respectively. Answers to questions rdaiiny to Fie/, 8 — (7) When the strap occupies — The lefc-hand extreme position. . 14*1 revolutions . 244 feet . 2 '45 revolutions . 42-3 feet Spiked lattice roller >) jj Hopper lattice roller )) )) Supply lattice roller 0'358 revolutions 6-3 feet The light-hiind exLreme position. G2*5 revolutions 1238 feet 1084 revolutions 187-6 feet 1*615 revolutions 27-9 feet (8) The parts aifected would in this case be the same as in question 7, each being increased in rate to the extent of f , or — Spiked lattice roller 30'58 revolutions 528-72 feet Hopper lattice roller >> » Supply lattice roller 5"31 revolutions 91-8 feet 0-791 revolutions 13-67 feet (9) In this case only the supply lattice would be affected, and this to the extent of Jj ; thus — Revolutions of supply lattice roller .... 0-492 Surface speed . . 8-5 feet (10) In this instance only the supply lattice would be affected, and this to the extent of |2 x l^, and therefore — Revolutions of supply lattice roller = 0*756 Surface speed = 13-67 30 COTTON SPINNING CALCULATIONS Calculations relating to the speed of the imrts found in Fig. 9. Eevolutions per minute of — m 1 u- 11 612 X 1 X 34 X 27 X 17 „ ^^„ The lattice roller = ^r;^- — — — -— ^ = 5*835 The surface speed of ) ^ 5- 835 X 3^^ X 2 2 the lattice in inches ) 7 62 X 40 X 33 X 20 = 55-015 1 St. Feedi^olleP 2nd. Pressure i;o*Ter 2V'y 612 revs. J per.min R C —.--.Right side Left side In aide Bottom Cone '"^-i "^20 Fig. 9. The first presser roller = 612x1x34x27x17x28 ^ ^ 62x40x33x20x35 ' The surface speed of the) ^ 4-667 X 3 '5" x 22 _ first presser roller in ins. ) 7 ~ 51'337 The lower feed roller = 612^^1 X^x2j 62 X 40 X 33 AND COSTS OF YAEN 31 The surface speed in) 6 -865 X 3^' X 22 ^ inches per minute ) 7 The second presser roller = 6 2 x 40 x 33~x~33 ~ '^'^^ The surface speed in) ^ 7-76 x 2|" X 22 ^ inches per minute ) 7 ~ The pedal roller = ^^'^ ^ L ^^ = 8'358 ^ 62 X 40 The surface speed in I _ 8'4 x 2f " x 22 _ inches per minute) ~ j — /ZUi Questions relating to Fig. 9. (11) What would be the effect of changing — (a) The 17 on the lower feed roller to 16 ? (h) The 27 on the pedal roller to 32 ? (c) The cone strap to the extreme loft on the cones, if their diameters at those points were — bottom, 3J ; top, 8^ ? Answers to questions relating to Fig. 9 — (11) (fl) The rate of the lattice roller would be reduced to — Eevolutions Surface speed in per minute. feet per minute. 5-592 52-95 (h) All the parts dependent upon the 27 wheel for their motion would be aflected directly as the change, namely — The lower feed roller to . ,, lattice roller to . ,, first presser roller to . ,, lower feed roller to . „ ^second presser roller to (c) Each of the rollers in Fig. 9 would have their speed changed to 31 7 ^ X ^ 3- X speed of part when the strap is in central position. Calculations relatiiuj to the speeds of the parts found in Fig. 10, the drivinc) of the heater being as given in Fig. 7. Eevolutions and surface speed per minute of — Topside ) _ 220x36x27x 5 x 13x13x24 ^4455^ shaft) 16x13x24x65x38x24 304 ievolutions SuTfice speed er minute. per minute. 8-136 76-68 6-916 65-27 5-531 60-84 8-136 76-68 9-19 79-4 32 COTTON SPINNING CALCULATIONS Bottom cage 1- 220x36x2 7x 5 Xl 3 x 13 X 24 X 24 X 40 X 14 X 44 16x 13 X 24 X 65 X 38 X 24 x 30 X 28 X 44 x 115 498960 = 2-039 ' = 102"'53 2128.115 Surface ] _ 2-039x 16"x 2 2_ speed j 7 _ 220 X 36 X 27 X 5 x 13 x 13 X 24 x 24 x 4 X 14 x 44 Top cage - 16x13x24x65x38x24 x 30 x 28 x 44 x 151 498960 , ...^Q = 3^1328 = ^ ^'^^ Too& Bottom Feedroller to the Beater 2j"dia, Cage A / Rollers /; '"'/"i "■■ 3"dia. // A/ .,i3" •, / Bottom Calander Shaft rop Shaft Fig. 10. Surface 1 1-5528 X 21" x 22 speed Cage rollers 1 = = 102"-485 220x36 x27x 5 xl 3x 13x24x24x40x14 16x13 X 24 X 65 X 38 X 24 x 30 X 28 X 20 178^50^ '' 1520 ' AND COSTS OF TArvN 33 Surface 1 _ 11-72 x 3" x 22 , , ^„ ^ speed) ^ = 110 -5 Bottom -\ ^ 220x3 6 X 27 X 5 X 13 x 13 x 24 x 24 x 40 feed roller] 16 x 13 x 24 x 65 x 38 x 24 x 30 x 28 _ 35640 -^28=^^^^ Surface \ _ 16*75 x2i"x 22 ,^,„_ speed/-" 7 =131 -b Exercises in Coxxectiox with Fig. 10. What would be the effects if — (a) The 44 wheel driving the bottom cage wheel was changed to 4G ? (b) The 14 wheel on the bottom feed roller was changed to IG? (c) The 24 wheel on the side shaft was changed to 22 ? Ascertain the wheels that would make the surface speeds of cages, cage rollers, and feed rollers as nearly alike as practicable without altering the rate of the latter. Calculations relating to the sjjceds of the parts found in Fig. 11. Eevolutions and surface speed per minute of — 220 X 36 X 27 X 5 x 13 x 13 x 27 X 25 x 33 16 X 13 X 24 X 65 X 71 X 21 X 25 X 151 = 2-203 Q , , 2-203 X 21" X 22 .,^n ,^ Surface speed = = =145 '45 rp, , . , 220 X 36 X 27 X 5 x 13 x 13 x 27 x 25 x 33 The bottom cage = — The top cage = 16 X 13 X 24 X 65 X 71 X 21 X 25 X 115 = 2-893 Surface speed = s- = 145"-51 ^, ,, 220x36x27x 5 x 13x13x27x25 The cage rollers = -^ — — ^ — ^, — ^j- — =-. — ^ — ^ ° 16x13x24x65x71x21x16 = 15-756 Surface speed = — = 148"-55 First or the top) _ 2 20x36x27x 5 x 13x13x27 ^^.^^ calender [ 16x13x24x65x71x23" n , . 9-207 X 5"-5 X 22 , .^^ i - Surface speed = ^ = lo9 -lo 34 The second calender = Surface speed = COTTON SPINNING CALCULATIONS 220x36x27x 5 X 13x13x27 16x13x24x65x71x22 9-626 X "5-5 X 22 ^ ^ggr/.g^ = 9-626 The third calender = ^ 20x36x27x 5 X 13x 13x27 ^^p.„3^ Surface speed = 16x13x24x65x71x21 10-084 X 5^^-5 X 22 ^ ^^^..^^ 23 The fourth or , 220 x 36 X 27 X 5 x 18 x 13 bottom calender ;■} = 16x13x24x65x71 = 7-843 ^, „ , 7-843 X 7" X 22 ,^r,>, ^^ Surface speed = _- = 172-55 mu 1 1, 220x36x27x5x13x21x17 „ ^„^ The lap rollers = -,n . .-..^..c ..n^. .r,. .^ 7^ = 7-179 Surface speed = 16x13x24x65x71x30 7-179 X 8r X 22 ^ ^^^,,.^2 Drafts in Openers.— In the processes embraced in spinning the cotton is attenuated in a somewhat graduated manner, until AND COSTS OF YARN 35 it is reduced to a siDScific weight per unit of length ; the extent of the attenuation applied, in each as well as in the collective processes, depending upon the ultimate fineness or count of the yarn required. The attenuation is increased with the fineness of the yarn, and it is distributed amongst the various machines in proportions which practice has proved most beneficial. A knowledge of the extent most expedient in each process, as well as between the various points in each process, is therefore indispensable. " Draft " is the term used to denote the attenuation or difference taking place in the unit of weight of the cotton in the various stages. It is used also in expressing the difference in the rate of movement of the parts of a machine. It denotes the amount of attenuation occurring between two points, which it is customary to express in terms of one unit of the preceding of the two points specified. Thus if the draft in an opener is said to be three, the rate of the delivery in terms of one unit of the feed is three, and therefore the cotton is elongated to an extent of three times its original length, and in consequence becomes at least one-third of the weight per unit of length fed. The several ways of proceeding to ascertain the amount of the draft are — (a) By timing the rate of movement of the respective parts. (h) By comparing the weight of the cotton per unit of length at the respective parts. (c) By calculating the relative movement of the respective parts by means of the connecting gearing. The methods (a) and (h) are, of course, only practicable when it is convenient to work the machines. The other method (c) necessitates particulars of the gearing only, and the draft can be ascertained at any time. It is the method most generally adopted, and is accurate. When it is inconvenient to obtain particulars of the connecting gear, an approximate result may be quickly arrived at by either of the former methods. The following calculations illustrate the methods (a) and (c), the speeds representing the former, however, being those already ascertained by calculating from the connection with the driving 36 COTTON SPINNING CALCULATIONS shaft, instead of by timing. Examples illustrating the application of the method (b) will follow. Calculations rclatinr/ to the drafts hetivcen the various con- ti(juous parts comprised in the opener, as represented in Figs. 7, 8, 9, 10, ajul 11. The draft between — The supply and bottom lattice (Fig. 8) — By the calculated! lS-5" _n.„-,c, surface speeds ) 10-94" or, by the connect- _ 85 x 78 X 7 X 23 X 17 X 20 x 20 x 5 .^ =G-714 ing gear J 12x1x9x55x79x48x48x5^, The lower hopper lattice and the spiked lattice — By the calculated surface speeds = nroTg^- = 5 "76 48 X 48 X 5\ or, by the connecting gear = ^q x"20'x~5^' "^ ^"^^ The spiked lattice and the feed lattice to the porcupine cylinder (Figs. 8 and 9) — By the calculated] 55*01 _ n.io surface speeds ) ~ 422*98 ~ By the connect-) 79 X5 5x9x 1 X 34x27x17x3 ing gear ( 17 x23x4x 62x40x33x20x 5>, ~ The feed lattice and first presser roller to porcupine cylinder (Fig. 9)- By calculated surface speeds = „,. = 0*93 28 X 3^" By the connecting gear = ^ ^ = 0*93 do X O The feed lattice and the first lower feed roller to the porcupine — 64'7 By calculated surface speeds = ,_ ^■, = 1*17 oo'Ol 20 X 3 By the connecting gear = -= = 1-17 AND COSTS OF YARN 37 The first lower feed roller and the pedal roller — By the calculated surface speed = ^. =1-11 S3 X 2'^ By the connecting gear direct = 5^^—^ "= 1'12 Z ( X o The pedal roller and the first bottom cage (Figs. 9 and 10) — 102'53 By the calculated surface speeds = rfKj^ = 1"-123 By the connecting gear direct _40x62x7x20xl5xl3xl3x24x24x40xl4x 44 x 16 34 X 1 X5x40 X 30 X 65x38x24x30x28x44x151x2^ = 1-423 The first bottom cage and the first cage rollers (Fig. 10) — By the calculated surface speeds = .. „-, .^ = 1*078 15 iu I' A' i. 115 X 44 X 3 69 ,. ^^ By the connecting gear direct = , , ,, or> v -,a ~ ri = l 08 •^ ° ^ 44 X 20 X 16 64 The first cage rollers, and feed rollers to beater — By the calculated surface speeds = =1*19 20 X 2' By the connecting gear direct = ^ . o" = 1"19 The feed rollers to beater and the second bottom cage (Figs. 10 and 11)— By the calcu- 1 ^ 119-78 ^ lated speeds) 131-6 By the connect- 1 _ 28x30x24x38x27x25 X 25 Xl6 ^ ^,^^ ing gear direct I 40 x 24 x 24 x 71 X 21 x 23 X 115 X 2.^ Second bottom cage and the second cage rollers (Fig. 11) — By the calculated surface speeds = ^ . ■,.. = 1"02 By the connecting gear direct = .)o^T('~x~ig ~ ^^'^ 38 COTTON SriNNING CALCULATIONS Drafts (continued) — First calender (top) and the second cage rollers — 159'15 By the calculated surface speeds = i-TnT^r = 1*07 By the connecting gear direct = g q y oq y o' r~ = 1 07 Second and first calenders — By the calculated surface speeds = ^t-q.-ip- — I'O-l^ 23 X 5"'5 By the connecting gear direct = oo y K".r . ~ I'OIS Third and second calenders — 174*30 By the calculated surface speeds = -r/(p7q-q = 1'047 22 X 5"'5 By the connecting gear direct = ^ ^777^ = 1*047 As. X 5 '5 Fourth and third calenders — 172*42 By the calculated surface speeds = frjA^on = 0*99 21 X 7" By the connecting gear direct = ^ ^777= = 0*99 Z I X 5 '5 Lap rollers and the fourth calender — 197*42 By the calculated surface speeds = ^ _ = 1*14 T> +r. r r . 71 X 21' X 17 X 8f , , , By the connecting gear direct = 13 x^rx"30"x 7 ^ The draft between the lap rollers and the feed rollers to the beater — By the calculated j. _ 197*42 _ surface speeds ) ~ TSTG ~ By the connecting ) ^ 28 x 30 x 24 x 38 x 21 x 17 X 8 j _ gearing direct i 40 x 24 x 24 x 13 x 71 X 30 X 2J ~ By the intervening I _ J 0*91 X 1-02 X 1*07 X 1*045 X 1*047 drafts 1 ( - j X 0*99 X 1*14 = 1*225 ' This dt'ficAency ix due to the drafts between the various parts being incompletely expressed. AND COSTS OP YARN 39 The draft between the lap rollers and the pedal roller — By the calculated I _ 197'42 _ ^-. surface speeds j 72'01 ~ By the connect- _ 4 x 62 x 7 X 20 x 15 x 13 x 21 x 17 X 8f _ ^.^.^ ing gearing direct j 34 X 1 X5x40x30x65 x71 X30x2| By the iuterven- ) _ f 1-423 X 1-078 x 1-19 X 0-91 X 1-02 x 1-07 ing drafts 1 j | x 1-045 X 1-047 X 0*99 X 1-14-2-30 The knowledge of the amount of the draft between the various parts in a machine enables the relative weight of the cotton at each point of its progress to be ascertained, provided any loss between the points in question is allowed for. Thus, if in the opener in question, the laps made weighed at the rate of 12 ozs. per yard, and the visible and invisible loss therein amounted to 3 per cent., and the draft between the various parts is as calculated below, the weight per yard of the cotton delivered by the spiked hopper lattice would be — /Weight of 1 yard)^ , rper cent, of waste\ rthe draft between the \ of opener lap / "^ I extracted / ^ points in question (a) (b) (c) (d) and .-. (12-0 ozs. x V¥ ) X 2*72 X 1-12 x 1-17 X 0-13 the last four items being the respective drafts from the lap rollers to the spiked lattice : (a) that between the lap and pedal rollers ; (h) that between pedal and the lower feed rollers to the porcupine ; (c) that between the feed and lattice rollers to the porcupine ; (d) that between the feed and the spiked lattices. The answer is 5-74 ozs. The weight per yard of the cotton at the pedal roller would be— 12 ozs. + 3 per cent, lost on the original weight X draft or, 12 ozs. X Vr X 2'72 because the cotton composing the lap has been subjected to a loss of as 100 : 97, therefore that must be allowed for as well as ' This deficiency is due to the drafts hetween the various jjarts being incompletely expressed. 40 COTTON SPINNING CALCULATIONS the length, contracted to the extent of 2'72 times the length delivered, thereby increasing the weight to that extent. Thus — ■^c^ inn -> r-o ( thc Weight of tlic cotton 1 ^., __ , 12 X V? X 2-73 = {f^^ by the pedal roller (x) } = ^^'^^ ^^'- P^^' ^^^ The weight of the cotton at any other points may be similarly calculated, the weight being only approximate if the loss is unknown. The following answers relate to the weight of the cotton at the various points, the loss between the pedal roller and first pair of cages being assumed as 2 per cent., and 1 per cent, between the first and second pairs of cages. The working of this question is given so that the student may accustom himself to the working of such exercises. The weight of the cotton at — Feed lattice to porcupine 44"1 ozs. Pedal roller „ .... Ans. = 33'68 „ (Working.) Let x = weight of the cotton at the pedal roller — — A-rjT = weight of cotton at delivery .'. --x-„^-- = 12 ozs. .-. ^ ^^y^" = 12 ozs. .-. « = 12 X -Vr X 2-72 = 33-68 ozs. Ans. First pair of cages A ns. = 23*1 ozs. Feed rollers to beaters Ans. = 18*2 ,, Second pair of cages .4/is. = 19'8 ,, Between calenders 3 and 4 . . . Ans. = 13*68 ,, It is customary to alter the draft by means of the wheels on the side shaft, also slight alterations by adjustments of the cone strap. Exercises in Respect of Drafts in the Opener as per Details in Figs. 7, 8, 0, 10, and 11 iNCLUsivF, WITH Answers appended. Find the drafts between the following parts by gear direct : — (11) Spiked lattice and pedal roller. Ans. 0-171. (12) Spiked lattice and feed roller to the beater. Ans. 0-31. (13) Spiked lattice and lap rollers. Aiis. 0-212. AND COSTS OF YAllN 41 (14) Pedal roller to cylinder and feed rollers to beater. Aiis. 1"81. (15) Pedal roller to cylinder and second bottom cage. Ans. 2*02. (IG) Pedal roller to cylinder and bottom calender. Ans. 2"38. (17) Feed rollers to the beater and the first calender. Ans. 1*1. (18) Feed rollers to the beater and the lap rollers. Ans. 1"5. (19) The second bottom cage and the lap rollers. Ans. 1"35. (20) First calender and the bottom calender. Ans. 1'08. (21) Assuming that this opener produced laps which weighed at the rate of 13-5 ozs. per yard, what change in that weight would arise from each of the following alterations : — (a) Tiie 30 cross-shaft bevel changed to 27 ? (b) The pinion on the bottom cone to 22, and that driving it on the side shaft to 38 ? (c) The 5-inch pulley on the beater shaft to 6 inches? Ans. 12-15 ozs. ; ll"G6ozs. ; 13-5 ozs. (22) What changes would produce a lap weigliing 10 ozs. per yard, assuming that with the gearing as in the figures the lap made weighs 12 ozs. per yard? Scutchers. The Particulars of Driving. — Speeds of the parts in the scutcher (Fig. 12). In this figure B is driven by a belt from a 25 -inch pulley on a counter shaft, and the latter is fitted with fast and loose pulleys, 15 inches in diameter, and these latter are driven by a belt from a 32-inch diameter drum on the line shaft, which makes 220 revolutions per minute. The revolutions per minute of the various parts, together with the calculations, are as follows : — Beater shaft (B) = ^^^ "^ 15 x 10 = ^^^^* ^ 220 X 32 X 25 X 5 „^^ . Fan = -^ = = 838-1 15 X 10 X 7 ^ , „, 220 X 32 X 25 X 6 „„„ ^ Cross shaft = — —r — -- = 586*6 15 X 10 X 12 Driver cone 1 ^ 220 x 32 X 25 X 6 X 6 .]r drum (D) ( 15 x 10 X 12 x 5| ~ Feed lattice ^ 220 x 32 x 25 x 6 x 6-5 x 4-5 X 1 X 39 _ ^ . ^o roller (F) j 15 X 10 X 12 x 5-5 x 4-25 X 88 X 60 ~ Surface rate = = 51"-121 42 COTTON SPINNING CALCULATIONS AND COSTS OF YARN 43 p,, ,, 220x32x25x 6 X6-5X4-5 xl „,,„ Pedal roller = — --, — ^-^^ — -- — — — — -^ = 8'342 15 X 10 X 12 X 5-5 X 4-25 X 88 Q , , 8-342 X 2" X 22 „_„ ._ Surface rate = „ = 52 -435 Lap motion ) _ 220^ 32 x 2 5 x 6 x 8 _ oo , p shaft (L) j - " 15 X 10 X 12 x~20 ~ ^"^^'^ ^ ,, .^, 220x32x25x6x8x13x20x32 ^ ^^ Bottom cage (C) = r-= — :r^ — r?^ — ^rr: — =- — — i — -— = 3*87 ^ ^ ^ 15x10x12x20x71x74x96 Surface rate = - ^ - ^ ^^" ^ '^^ = 145"-988 Top cage (C) I 220x32x25x 6x8 xl3x20x 32 _o.,-... (19") ) 15x10x12x20x71x74x154" c; , , 2-413 X 19" X 22 ,,,„.. Surface rate = -^ = 144-09 rr, , , ,,-,,, 220x32x25x6x8x13x20x19 ,^ ^^^ Topcalender(21) = i5>riOxT2^20-x-7rx 74 x21 = ^^"^^^ Surface rate = ^^'^^^^^"^^^ = 165"-094 Eevolutions and surface speed per minute of — Bottom calender] ^ 220^x 32 x 25 X 6 X 8 x 13 x 20 , , ., „ (19-32) j 15^00^12X20^71X74" '^^^' Surface rate = ^^^^1'-^^^ = 182-474" Lap rollers (9.V') ^ 220x32x25 x 6 x 8 x 13 X 11 diameter) ' ( 15x10x12x20x71x74" ^^^^^^* Surface rate = 6:38Ix_9:5:^2 ^ ^^^..^^^ Drafts between — Pedal roller and feed lattice— («) By gear direct = |^-^ = 1-025 "^ ^ 39 X 3 52*435 {b) By the surface rates, already calculated = ^it^tt^ = 1'025 ol'lzl 44 COTTON SPINNING CALCULATIONS Bottom cage and pedal roller — I A = 88x4|x5^x 8 X l3x20x32x 12 " diameter ^'^ 1 X 4.1 X 6.1 X '20 X 71 X 74 X 96 x 2" diameter ~ ^^ Top cage and bottom cage — , . 154x12" . _^„ ^'^^ = 144^09 = ^^^^ Bottom calender and bottom cage — / ^ 96 X 5 ^ ^^^ (^^ = 32^ri2 = 1'^^ ^^^ 145-988 --^^^ Lap rollers and bottom calender — "> 2 X 74 X 5 = ^'"^ ,,, 190-696 ,„,^ (''^ r82^74 = 1 °^^ Lap rollers and bottom cage — ^ . 96 X 74 X 11 X 91 , ^^^ r/A 190-696 ^''^ 145^988 = ^ ^^^ Lap rollers and pedal roller — (a) 88 X 4| X 5^ X 8 X 13 X 11 X 9.1 _ _ __ ^ ^ ■ 1 X 41 X 61 X 20 X 71 X 71 X 2 - "^ ^"^ (h) 190-696 Lap rollers and lattice roller — 60 X 88 X 4j X 51 X 8 X 13 X 11 X 9i _ ^ _^ ^ ^ 39 X 1 X 41 X 61 X 20 X 71 X U>rd ~ "^'^"^ (jb) 190-696 _ ^' 51-121 "^^^ AND COSTS OF YARN 45 Exercises ix respect of the Parts in Fig. 12. Exercise 1. — What sizes of — (a) Beater pulley would be required to give lOGG revolutions of that part per minute ? (h) Counter shaft drum (25 inches) would be required to give 12G6 revolu- tions of beater shaft per minute ? (c) Pulley on the fan shaft would be necessary to give 1173/r revolutions of fan per minute ? (d) Pulley on the beater shaft would be necessary to drive the fan 1675 revolutions per minute ? (e) To what extent would the weight produced by the machine be affected by the alterations (a) and (b) respectively ? (/) What changes respectively in the gearing would be expedient after making the alterations (a) and (&), if it was required that the weight produced in a given time remain as before the alteration ? Exercise 2. — What would the draft in the machine (Fig. 12) become, if the following alterations were made in the gearing : — (a) The 8-inch pulley on the cross shaft changed to 9 inches and 7 inches successively ? (b) The 65-inch pulley on the cross shaft changed to 6 inches and 7 inches successively ? (c) The 65-inch and 8-inch pulleys, both on the cross shaft, are changed to 7 inches each ? Exercise 3 — (a) Ascertain the weight, in pounds, per lap in each of the cases (a), (h), (c). Exercise 2, and also the number of laps made in 10 hours, assuming they measured 36-7 yards, and averaged 22 lbs. 15 ozs. each, with the gearing otherwise as per Fig. 12. Allow 10 per cent, for lost time. (b) What change in the sizes of the 6|-inch or 8-inch pulleys on the cross shaft would be necessary to produce a lap 12 ozs. per yard, if that made with the gearing, as per Fig. 12, weighed 10 ozs. per yard? Also, state the differ- ence in the length and weight, in both instances, which would be caused by the change. (c) What effect, upon the output of this machine, would result from an alteration in the position of the strap on the cones ? Assuming the sum of the diameters of the cones at opposite points are 8f inches, and the strap is on a part of the driven cone 4 inches in diameter, what would be the weight per yard of the lap made, if that produced with the gearing, as per Fig. 12, was 10 ozs. per yard ? (d) If the lap made in a machine, geared as per Fig. 12, averaged 36*7 yards and weighed 22 lbs. 15 ozs., and the loss in the process was 2 per cent., and the number of laps used at the feed 4, what should* be the weight per yard of each of the latter ? 46 COTTON SPINNING CALCULATEONS AND COSTS OF YARN 47 Exercises in Calculatlno the Speeds and Duafts of the Various Parts IN THE Scutcher (Fig. 13). Calculate the revolutions per minute of the following parts. The numerals signify the teeth contents in wheels and diameters of pulleys and other parts in inches. Exercise 4 — ■ (a) Fan (5 inches). Ans. 2880. lb) Lap motion shaft (15-30). Aiis. 400. (c) Side shaft (30-60). Ans. 400. (d) Driver cone (4^ inches). Ans. 800. (e) Driven cone (5 inches). Aiis. 720. (/) Feed roller (30-80). Ans. 9. (</) Feed lattice (5^ inches diameter). Ans. 4J-Y- (^i) Top cage (240)"". Ans. 4-842. (0 Bottom cage (190). Ans. 6-116. (/) Cage rollers (20). Ans. 45-4. (k) First calender (23-5 inches). Ans. 23-15. (l) Second calender (22-48-5 inches). Ans. 24-2. (m) Third calender (21-5 inches). Ans. 25-35. (70 Fourth calender (29-70-7 inches). Ans. 18-36. (o) Lap rollers (35-120 and 35). Ans. 14-28. Exercise 5. — Calculate the drafts between the following parts in the scutcher (Fig. 13) : — (a) Feed lattice and feed roller. Ans. 1-0. (b) Feed roller and bottom cage. Ans. 4-3. (c) Top and bottom cages. Ajis. 1-0. (d) Bottom cage and cage rollers. Ans. 0-976. (e) Bottom cage and first calender. Ans. 1-04. (/) Cage rollers and first calender. Ans. 1-067. {g) First and second calenders. Ans. 1-045. (h) Second and third calenders. Ans. 1-048. (i) Third and fourth calenders. Ans. 0-987. (/) First and fourth calenders. Ajis. 1-11. (k) Fourth calender and lap rollers. A^is. 1-0. (J) First calender and lap rollers. Ans. 1-11. (to) Feed lattice and lap rollers. Ans. 4-763. Exercise 6 — (a) Give the drafts, from 4-763 to 3-2, which the following range in sizes of driver and driven draft change wheels would obtain, limiting the range in the driver 30-45 with 30 driven, and in the driven 20-30 with 30 driver. (b) What single and pairs of draft change wheels, within the following sizes, driver 20-40, driven 20-50, will give drafts nearest 4-5, 4-1, 3-8, 3 5, 3-25, 3-0, and 2-85 respectively ? 48 COTTON SPINNING CALCULATIONS Answers to Exercise G (a) ■ Driver 31 32 33 34 35 36 37 38 Draft . 4-Gl 4-5G 4-35 4-2 4-08 3-97 3-8G 3-7G Driver 39 40 41 42 43 44 45 Draft . 3-GO 3-57 3-48 3-4 3-32 3-24 3-17 Driven 30 29 28 27 2G 25 Draft . . 4-76 4-6 4-45 4-28 4-13 3-97 Driven 24 23 22 21 20 Draft. 3-81 3-67 3-5 3-34 3-17 Ans^cers to EoL ercise G (h) — 4-5 : driver driven' 4a- 51 4 5) 23 3-25 = ff 4-1 = = u 3-0 = sf; ft 3 8 = -24- 2 7 -30? 35 ;f§ 3-5 — 3 e . 25 — 48 5 34 2-85 = §1 The Hunting Cog Measuring or Length Motion used in Openers and Scutchers. — In Fig. 14, K and A represent the calenders and C=^ Fig. 14. also the connecting wheels ; H is the drop-shaft wheel ; G the drop-shaft lever, Gi being its pivot, g is a projection of G sup- ported by the lower part of catch lever F, F is pivoted on P and AND COSTS OF YARN 49 coupled to the lower part of lever D by Di, D having its fulcrum at E. The spring I presses against D, forcing the wheel C, which is loose upon a stud attached to D, to gear with wheel B, the latter being fixed upon the shaft of the calender A. E and B are projections from the sides of the wheels C and B, which are in gear. When the projections meet the wheel C is forced out of gear with B, this action causes the levers D, Di, and F to release g, and consequently G falls to T, thereby disengaging H from J, and, since the latter is driven by the former, J ceases to rotate. The fall of the lever G disengages the feed-motion clutch by rod connections with G shown at point Z. The lap continuing to rotate after the calenders have ceased delivering effects the severance and completion of the lap. The length of the lap made is governed by the revolutions which the wheel B makes in causing its projection to have contact with E, on C. The revolutions of the wheels B and C, per lap, are the least whole numhers which express the relation of their tooth contents, their relative revolutions being inverse to those numhers. Thus, if B is 21, and C ranged from 71 to 81 teeth respectively, the revolutions of these wheels, per lap, would be as given in the first part of the table on p. 50. If B had 72, and C ranged from 71 to 81 teeth, then their revolutions per lap would be as given in the second part of that table. If C had 80 and B 2 teeth, then their respective revolutions would be 1 and 40. Should C be any number which has no common divisor between itself and unity, then, if B contains less teeth than C, the revolutions of B per lap would be the same as the teeth contents of C. Assuming the diameter of the calender 5 inches, then the length of the lap would be — 5" X 3*1416 X revolutions of B per lap , 33 i '-^ = yards or, revolutions of B per lap X 0'4363 yard 50 COTTON SPINNING CALCULATIONS Ratio of their teeth j Sizes of the wheels Relative rate of contents expressed ' (in teeth). their rotation. in smallest whole numbers. Revolutions of B per lap. 1 71 Length of the lap in yards as ascettained by calculation. B. ! c. B. c. B. C. 71 21 71 71 21 21 30-98 21 72 72 21 7 24 24 10-47 21 73 73 21 21 73 73 31-85 21 .74 7i 21 21 74 74 32-29 21 75 75 21 7 25 25 10-91 21 76 76 21 21 76 76 33-16 21 77 77 21 3 11 11 4-8 21 78 78 21 7 26 26 11-34 21 , 79 79 21 21 79 79 39-47 21 1 80 80 21 21 80 80 39-90 21 81 81 21 7 27 .7 11-77 72 71 71 72 72 71 71 30-98 72 , 72 72 72 1 1 1 0-4363 72 1 73 73 72 72 73 73 31-85 72 74 74 72 36 37 37 16-14 72 75 75 72 24 25 25 1091 72 76 76 72 18 19 19 8-29 72 77 77 72 72 77 77 38-59 72 ' 78 78 72 12 13 13 5-67 72 79 79 72 72 79 79 39-47 72 80 80 72 9 10 10 4-36 72 81 81 72 8 9 9 3-96 Example. — If C is 78 and B 41, and the diameter of the calender 5 inches, and the draft between this calender and the lap rollers 1 '045, then the approxi- mate length of the lap ^YOllld be as follows :— The ratio of the tooth contents of C and B cannot be expressed in less whole numbers, and hence B will make 78 revolutions per lap, .*. 78 X 5 X 3-141G x 1-045 = length of lap in inches (approximate) = 1280-36 inches = 106-7 feet It is found that, when the lap is verj- thick, the lap exceeds somewhat the calculated length ; but as this discrepancy^ is the same in respect of each lap of the same weight, it is generally neglected, and the calculated length taken as the actual. The advantages of the hunting-cog motion is that it obtains the same length on each lap, and this cannot be claimed in respect of the other motions. This arises through the slow and irregular disengagement of the knocking-off catch in the latter. Laps of a length representing any number of revolutions of the operating calender can be made by this motion. AND COSTS OF YARN 51 EXEKCISE 7 — (a) How many revolutions would B make, and what length of lap would result, if B and C were 41 and 81 respectively and calender 5 inches diameter ? Ans. 106 feet. (b) What length of lap would be made if B had 42 and 81 teeth when the calender B is 5 inches in diameter? Ans. 35-3 feet. (o) What sizes of B may be used for a lap of 36*2 yards if C had 83 teeth when the calender B is 5 inches in diameter ? Ans. 1-82. Platt's Knocking-off Motion In Fig. 15, K is the bottom calender and A is a single worm secured to it ; B is a worm wheel driven by A, and C a pinion fixed upon the axis of B ; C drives the "knocking-off" wheel D, the projection E on D pulls the catch F and the lever G, to which it is attached, in passing that point. This movement moves the lever G to the right on its pivot X until G ceases to support H. The latter is the drop-shaft lever and in consequence of the withdrawal of the support G, the drop- shaft wheel is disengaged from driving the calenders and other parts dependent upon them for their motion, and hence, delivery ceasing, the lap is completed. To start a new lap, G is raised at a point on the left to enable the clearance of the catch F from E, F is supported by a finger of the right hand, whilst the left lifts the drop lever H, when the weighted portion of G, to the left of X, causes it to move into a supporting position for H. This action engages the drop-shaft wheel, and sets the delivery and feed parts in action. The length of the lap will vary according to the revolutions which the calender makes in turning the wheel D one revolution. The gear may be as follows : — Bottom calender, 7 inches diameter ; A, 1 ; B, 25 ; C, 18 ; D, 48. The revolutions of A per one of D will therefore be — Fig. 15. 48 V 18 -^ 25 1 12 IS and the length of the lap in yards 1 = 1200 .7" X 3-1416 = 40-724 18 36 This type of length motion tends to the production of laps 52 COTTON SPINNING CALCULATIONS slightly varying in length. This arises from the slow move- ment of part G during its "withdrawal, and the tendency of its supporting surface to wear smooth and somewhat rounded ; this, assisted by the vibration, causes the supporting part G to fall away at slightly varying intervals 'measured in revolutions of the calender. Exercise 8. — Calculate the length of the laps — (a) When C is 16, 17, 19, and 20 respectively. Ans. 45-75, 43-15, 38-6, 36-15 yards. (i) When the following wheels are used together instead of those previously given: A, 1 ; B, 24; C, 17 ; D, 50. A7is. 43-15 yards. (c) When B is altered to 24? Ans. 39-1 yards. {d) When D is altered to 50? Ans. 42-5 yards. Exercise 9 — If a lap 50 yards long is required, what single wheel would give the nearest result? Ans. Changing D to 59. Exercise 10 — If a lap 48f j\irds was required, what size of C should be used ? Aiis. (5). Exercise 11 — (a) What length of lap, in yards, would be made if the hunting-cog lap length motion wheel on the top calender contained 82 and the wheel on the knockiug-off lever 83 teeth ? Ans. 40-21. (6) Find the time taken to make a lap 40-21 yards in length, Ans. 3 845 minutes. (c) What would be the weight of one lap and also the production in lbs. per 10 hours, if 2 per cent, waste was extracted and the time lost in taking out the laps and other incidental stoppages equals 8 per cent, and the weight of the four laps comprising the feed each average 11-8 ozs. per yard. Assume the length of the lap 40-21 yards. Ans. 39 lbs. ; 6006 lbs. (d) What changes in the gear would be best to reduce the output to a normal amount, say to 3000 lbs. per 10 hours, v.-ithout changing the count of the lap ? Ans. Keduce size of 8 inches, and increase size of 24 inches in con-esponding proportions ; or 8 inches to 6 inches, 24 inches to 30 inches. Practical Notes. Changes in the Weight and Count of the Laps made by Openers and Scutchers. — The position of the cone strap is automatically controlled by the feed regulator. To facilitate adjustments in the weight of the lap, as circumstances demand, an adjusting screw connection is provided. This latter, and changing the AND COSTS OF YARN 53 draft gear, are the means of controlling the draft, and therefore of the weight and count of the lap made. The range of adjust- ment practicable, in respect of the draft by gearing, is unlimited ; but that by the adjustment of the cone strap is very limited, and should only be availed of for temporary adjustments. The best position for the cone strap, when the feed is of the mean or normal weight, is at the centre of the cones. This secures the widest and most useful range of action of the cone strap, adaptable equally toward light and heavy variations in the feed. When, by temporary adjustments, so often necessitated by varia- tions in the character of the cotton, and actions of the machine, common in ordinary working, the cone strap has been gradually moved and settled in a position otherwise than central, steps ought to be taken to alter the draft to an extent which will restore the cone strap to the centre position, or otherwise the efficacy of this part of the machine is interfered with. The system of connecting the feed and delivery parts, in these machines, by belt, is being superseded by rope or tooth gear. The method shown in Fig. 12 is not always satisfactory. Variations in the slippage of the above-named straps affect the draft, and add to that arising from the cone strap. Positive driving reduces the possibilities of such defects without intro- ducing any disadvantages. Fluctuations in the draft are also often occasioned by variation in the slippage of the feed lattice ; too highly tensioned or slack lattices, lattice roller bearings out of alignment, and obstructions about these parts, binding of the lattice against the sides, these are amongst the chief causes of variations in the weight and count of the lap. The system of connecting the feed lattice rollers by tooth gear should receive consideration whenever the variations in the weight of the laps is unsatisfactory and cannot be eliminated. Productions, Speeds, and their Controlling Factors. — In the spinning of coarse and medium counts of yarn from American and similar and lower types of cotton, exhaust openers are extensively used. In these machines the practice of dispensing the lap measuring and " knocking-off" motion is extensive. The advantages of such practice are, the elimination of the 54 COTTON SPINNING CALCULATIONS thick and thin place, usually following the stoppage, and in- creased production ; it is also a deterrent towards dilatoriness on the part of the attendant. Productions ranging as high as 40,000 lbs. per week of 55?, hours are not uncommon under such conditions. The rate of delivery ranges up to 30 feet per minute, and the rate of the feed about one-third of that amount. The weight of the cotton delivered ranges to 0*75 oz. per yard per inch of width, and that of the feed 2-5 ozs. per yard per inch of width. The sizes of ^feed rollers are from 2j inches to 3 inches in diameter. The highest surface rates of beating instruments range up to 10,000 feet per minute. Creighton porcupines up to 1000, small porcupine cylinders up to 1100, porcupines (discs) 900, large porcupines (36 inches and upwards) to 600, three-bladed beaters to 1250, two-bladed beaters up to 1500 revolutions per minute. Fans range up to 2500 revolutions per minute. The Controlling Factors in respect of the Parts and Speeds Named. — Small feed rollers are only adapted for light feeds at low rates and pressures. Feed rollers which have insufficient holding power depreciate the opening action by allowing "plucking." Overweighting in order to secure increased pressure — better holding power — has the same tendency. High rates of feed and beating, as well as heavy feeds, require larger feed rollers irrespective of the length of the staple. Too quick and over- feeding produces an excess of good cotton with the droppings, and interferes with the opening and cleaning actions. The sizes of feed rollers are from 2 inches to 3 inches diameter ; 21 inches are only suitable when the feed is light, slow, and the pressure moderate. High speeds, accompanied by a heavy feed and pressure, necessitate rollers 2| inches to 3 inches diameter ; 21 inches are only adapted for moderate conditions. Too close setting of these tends to weakening the fibres, whilst the opposite causes a stringy tendency in the appearance of the cotton. When large rollers are used {^■ inch would be satisfactory for the heaviest feed. With small feed rollers distances less than ^ inch are doubtful, AND COSTS OF YARN 55 High rates of beating cause good cotton to be forced through the beater bars, imparts a curly appearance, and also weakens the fibre. Overscutching is distinguished by the development of the curling tendency. There is a great variation in the rates at which fans are worked. This arises from constructional differences in respect of the exhaust trunks, passages, flues, etc., and dimensions of the fans. Deficient fan rates are signalized by the cotton being overscutched, desultory movement of the cotton from the beaters to the cages, presence of good cotton amongst the droppings. Too high rate of this part is distinguished by the rapid flight of the impurities along the passages, compact state of the cotton collected on the cages, absence of fine light impurities in the clearing casements and its presence in the cotton, low percentage of impurities extracted. Miscellaneous Questions appertaining to Opening and Scutching. (12) What number and weight of laps would be made in 10 hours imder the following conditions ? — 4 laps comprise the feed in the scutcher, and these average 10 ozs. per yard each ; the draft in the machine is 3, and the loss H per cent. Tlie laps made are 42 yards long. The lap rollers are 9 inches in diameter, and make exactly 9 revolutions per minute, 30 seconds being lost at the completion of each lap. Ans. 108 ; 3720 lbs. (13) How many scutchers, woiking under the conditions given in the last question, would be necessary to supply the laps for 108 cards, assuming each card produced 120 lbs. of 0-2 hank sliver and made 5 per cent, waste. Ans. 4. (14) What should be the length in yards, the weight in pounds, and the number of laps made per 10 hours, if 4 laps, each weighing 10 ozs. per yard, form the feed in the scutcher geared as in Fig. 12, and the time lost altogether equals 10 per cent. ? Ans. 10-456 ozs. ; 2860 yds. ; 1896 lbs. Exercise 15 (Speeds). — Calculate the revolutions per minute of the principal parts in Fig. 13. Answers — Cross shaft, 400. Top cage, 4-84. Fan shaft, 2880. Cage rollers, 45-4. Side shaft, 400. First calender, 23*15. Driver cone, 800. Second calender, 24'2. Driven cone, 720. Third calender, 25-35. Feed roller, 9. Fourth calender, 18-36. Lattice roller, 4-9, Lap rollers, 14-28. Bottom cage, 6-11. 56 COTTON SPINNING CALCULATIONS Exercise 16 (Drafts).— Calculate the drafts between the following parts in Fig. 13 : — Lattice and pedal rollers. {Ans. 1.) Pedal roller and bottom cage. {Ans. 4-3.) Bottom cage and cage rollers. {Ana. 0"97G.) „ „ top calender. {Ans. 1-04.) First and second calender. {Ans. 1"045.) Second and third calender. {Ans. 1-048.) Third and fourth calender. {Ans. 0-987.) Fourth calender and lap rollers. {Ans. I'O.) Production in pounds in 10 hours' uninterrupted working, assuming the lap weighs 5250 grains per yard. {Ans. 5050.) Also, the draft between the feed lattice and lap rollers. {Ans. 4-76.) Also, tlie weight, per yard, of the cotton fed, assuming the lap produced to weigh at the rate of 5250 grains per yard, allowing 2 per cent, for loss in waste. {Ans. 25,500 grains.) Card Calculations. Fig. 16 represents the gearing common in cards of the revolving flat type. In the different makes of these machines wheels and other parts of varying dimensions are adopted, to adapt them for the conditions under which they work. The subtended calculations relate to the speeds of all the parts which they contain ; they are arranged in the following instances, as far as convenient, in progressive order. Slippage and thick- nesses of belts and ropes have not been taken into consideration in these calculations, but it is advisable to do so in practice. In belt drives, under bad conditions, this is sometimes considerable, but under fair conditions should not amount to more than two or three per cent, at each point in transmission. The actual speeds will be, therefore, somewhat less than the calculated. The speeds given are those in common use in treating ordinary Egyptian and the better classes of American cotton. The line shaft from which the strap driving the card, in the figure, is driven is assumed to make 220 revolutions per minute, and the drum upon it to be 12 inches in diameter. The dimensions given refer to the diameters in inches in respect of pulleys, or teeth in cases of wheels. AND COSTS OF YARN 57 58 COTTON SPINNING CALCULATIONS Details of calculation. Lap roller — 220xl2xl8x 5 X 28 X 40 x40x 14 Xl7 15x 7 Xl0xl00x216x40xl20x48 0-4848 X 6 X 22 7 The feed roller (120 x 17 X 21")— 2 20xl2xl8 x 5 X 2 8 X 40 x4 0x 14 15 X 7iri0 X 100 X 216 X 40 xT2d 1-369X 2i"x22 The lickerin (7" X 5")— 220 X 12 X 18 15 X 7 452-57 X 9" X 22 The cylinder (15" x IS" X 50" x GJ")— 220 X 12 . 15 " 176 X 50" X 22 The flats (40 X 12): hero, in estimating the surface movement, it is assumed that the distance from centre to centre of the flats measures IJ inches, and are driven by a wheel containing 12 teeth, eacli of which engages a " flat." The worm, driving the worm wheel (40), has a double tliread. 220 X 12 X 6^ X 1 X 2 _ 15 X 12 X 24 X 40 143 X 12 Xj£' ^ 720 X i X 1 Brushes : not shown. The driving gear for the brushes that clean the flats is not con- tained in the figure. The speed of that part varies ; under exceptional circumstances it is worked as high as 300 revolutions per minute. The normal rate of the ordinary brush is about 40 revolutions per minute. A patent com- bination brush — which gives encouraging results — is worked as low as 5 revolutions per minute. The stripping brush used in cleaning the cylinder and doffer is driven, during that Revolutions per minute. 0-4848 1-3G9 452-57 176 Surface speed per minute. In inches. 9-1413 In feet. 0-7GI7 9-G8 12786-98 27657 143 720 0806 1065-58 2304-75 3-574 AND COSTS OF YAEN 59 Details of calculation. operation, from a groove in the loose pulley on the cylinder shaft, the diameter being 15 or 10 inches, whilst that on the brush varies from 5 to 10 inches, thus giving — From- To- 220 X 12 X 15 15 X 10 220 X 12 X 15 _ 15x5 The doffer (21G x 9" x 40)— 220 X 12 X 18 X 5 X 28 X 40 _ 15 X 7 X 10 X 100 X 21G 176 X 26 X 22 ^ 15 7 The bottom calender (30 X ol)— 220J<J2J< 18 x5 J<^8_xj0 ^ 15 X 7 X 10 X 100 X 30 [Note. — The dofier wheel is here a carrier] 84-48 X 4 X 22 _ 7 The coiler delivery rollers (10) — 220x l2xl 8x 5 X 28 X40x31x20xl6 _ 15 X 7 XlOxlOO X 30 X 15 X 20 x 10 174-57 X 2" X 22 ^ 7 The coiler (106)— 220xl2xl8x 5 X 28 x40x31x20x 38 _ 15X 7 X10X100X30X15X20X10G The radius of the centre of the coiler tube at the point of exit is 3 inches — The distances traversed by this point = The can table wheel (82)— 220xl2x 18 X 5 X 28x ^OxS 1 x 20 X 16 15 X 7'x 10 X 100 X 30 X 15 X 20 X 48 ^ 16xl4 _ 48x8:i~" { Revolutions per minute. 264 528 11-73 84-48 174-57 62-5 Surface speed per minute. In inches. In f( et. 0;-)8-78 r9-898 1062-03 88-5 1097 423 91-452 1178 98-16 5-31 60 COTTON SPINNING CALCULATIONS Details of calculation. The number of coils laid per revolution of the cati — 625 3-31- Occasionally an alteration in the rate of the can is necessary through considerable chantre in thickness of the "sliver. If the 8])eed of the can is insufficient, the adjacent coils adhere instead of freely uncoiling. If the rate of tlie delivery is greater than the coiling rate, the sliver sticks to the sides of the can. and vice vend. The doflfer comb (4")— 220 X 12 X 18 X 1 2 15 X 6 X I ~ It is now usual to furnish this part with a stepped pulley, also the driver of this is like- wise stepped, so that the speed of the comb may be adapted to the rate of the doffer. The grinding disc, or roller, on the ' cylinder (5" x 7") — 220 X 12 X 18 6336 X 7 X 22 7 ~ The grinding disc, or roller, on the doflfer • the doflfer during grinding is driven from the IS-inch pulley on the cylinder during this action, the other gear being disconnected, the speed teing — 220 X 12 X 18 15 X 9 =" 352 X 26 X 2 2 7 ~ The direction of the cylinder when grind- ing is opposite to the normal working direction. The doflfer rotates in the same direction. This direction is opposite to that indicated by the bend of the card wire in both instances. ' The direction of the emery discs, or rollers, is opposing the movement of the parts to be ground. Revolutions ' per minute. Surface speed per minute. 18-8 In incbes. In feet. 1581 15 X 5 ~ I ^33-6 13,944 1162 352 28,704 2392 An increased or diminished rate of any of these parts may be obtained by altering the size of any of the wheels or pulleys, AND COSTS OF YARN 61 not a carrier, in the intercepting train, the effect being in direct ratio in case of drivers, and inverse when driven wheels or pulleys. The grinding of the flats is done at a similar speed to that of the cylinder, rollers being preferred to discs for this work. To alter the Speeds of the Various Parts. — The speed of the lap rollers may be altered by changing the 48, driven wheel, on the lap-roller shaft, and also by the 17, driver wheel, on the feed- roller shaft. The speeds of the lap and feed rollers may be altered by changing the 120, driven wheel, on the feed roller ; the 14, driver wheel, on the side shaft ; the 40, driven, on the side shaft ; and the 40, driver, on the doffer shaft. The speeds of the calender, coiler delivery rollers, coiler and can wheels may be changed by altering the doffer, 216, or the 30, calender shaft wheel. The speeds of the doffer, feed and lap rollers, calender and coiler delivery rollers, and also the coiler and can wheels, may be changed by altering the 5-inch driver pulley on the lickerin shaft, the 10-inch barrow pulley (driven), the 28 driver wheel on the hub of the latter, the 100 and the 40 driven and driver respectively. All these are connections in the train driving the doffer from the lickerin. The speeds of all the above parts may be changed by any alteration which increases the speed of the lickerin. In the event of a change in the speed of the lickerin being required without change in the speeds of the parts driven from it, it would be necessary to alter the connecting train at some point between the lickerin and the doffer wheel, inversely to the former change. Alteration in the movement of the flats may be effected by changing the 6^ -inch driver on the cylinder shaft, or the 12- inch driver pulley on the flat-motion shaft, or the double, for a treble, worm. 62 COTTON SPINNING CALCULATIONS Exercises ke Alteration of Speeds of Various Parts. Exercise 1. — If the card cylinder makes 178 revolutions per minute when its fast and loose pulleys are 16 inches in diameter, at what rate would each of its parts work after changing the fast and loose pulleys to 18 inches diameter ? Answers — Cylinder, 158'2. Coiler, 50-6. Lickerin, 402-2. Can wheel, 2-94. Doffer, 10-43. Doffer comb, 1408. Feed roller, 1-217. Stripping brush, 235-470. Lap roller, 0*431. Grinding discs, 563. Calender, 75-1. Doffer (when grinding), 313. Coiler delivery rollers, 155-18. Flats (inches per minute), 1-589. Exercise 2. — What alterations would be necessary to restore the speeds of all the parts implied in the last question, excepting the cylinder, to the original rates ? Answer's — 18-inch pulley driving lickerin to 20-25 inches. 7-«inch pulley driving barrow pulley to Gfi inches. 18-inch pulley on cylinder driving the doffer comb to 20.j; inches, or 6-inch pulley to 5 j inches. 65-inch pulley on the cylinder driving the flats to 7-31 inches. 5-inch pulley on the grinding disc to 4r^ inches. Exercise 3. — A card having a doffer 24-75 inches diameter, making 18 revolutions per minute, produces 550 lbs. of sliver per week. The driving pulleys are 16 inches diameter, and the cylinder makes 180 revolutions per minute. What size of pulleys would be needed to reduce the speed to 160 revolutions per minute ? What effect would this change have upon the revo- lutions per minute of the doffer as well as upon the length and weight produced per week ? A71S. 18 inches ; ^J- less length ; 488'^ lbs. per week. The Drafts between the Various Parts, how ascertained. — The draft may be ascertained by coraparing the weight per unit of length of the cotton at the different points in the machine ; also, by timing the speeds of the respective parts and ascer- taining from this their ratio; and again, by calculating the mechanical value of the connecting train of gear and dimensions of surface. It is preferable wherever possible to do this by the latter system, as it furnishes the most reliable data. The two other ways serve very well in ascertaining approximate results, and also in checking the calculated draft. AND COSTS OF YAllN 63 The results given below are arrived at, from, (a) the calculated speeds, as ascertained in the previous calculations ; (b) the connectional gear and sizes of the surface. The drafts between — Lap and feed roller— / N 9-68" , .. Feed roller and lickerin— (a) i?^^^^ = 1321 9-68 ,. 120^x4^x216x100x10x9 _ -,o„-, ^ ^ 14 X 40 X 40 X 28 X 5 X 2 j ~ "^"^^'^ Lickerin and cylinder — Flats and cylinder — 27657 (-) ^;;l = 15476 .J 40 X 24 X 12 X 50 X 22'^ ^ ^ irxT~>r6i X llx 12 X 7 "" ^^^ 958-78 Cylinder and doffer— («) ^'-^^ = 0-0346 V y 26757 " ^^^^ ,j 18X 5 X 28 X 40 X26-- _ ^ ^ 7 X 10 X 100 X 216 X 50" ~ " ^"^"^^ Doffer and calender — , ^ 1062-03 , ,^„ ^"^ 958-78 = I-IO^ 46 COTTON SPINNING CALCULATIONS Calenders and coiler delivery rollers — , , 1097-423 , _^.3 ("> 1062^)3 = 1 ^^^ 31 X 20 X 16 X 2" _ ^^^ IS'x 20 X 16 X 4" - ^'^^ The Drafts between the Various Parts, how altered. — It will be seen from the foregoing that the drafts between any of these parts may be altered by changing the size of any driver, or driven wheel, comprised in their connectional gear. Increasing the size of a driver increases the rate of the part nearest the feed, of the two parts concerned, and therefore reduces the draft, and vice versa. Altering the driven wheels has the inverse of the aforementioned effects. To ascertain the draft between other points than those given — which are those contained in the adjacent parts progressing through the machine — all that is necessary is to multiply together the intervening drafts between the parts involved. Thus— The total draft, i.e. between the lap and coiler delivery rollers — (a) = 1-04 X 1332 X 2-16 X 0-0346 X 1-107 X 1-033 = 118-4 By comparison of the surface speeds of these two parts — _ 1097-423 _ ^^^ -^1413^-^^^ By the connectional gear and sizes of parts — _ 48 X 12 X 40 X 216 X 31 X 20 X 16 X 2" ^ ^"^^ ~ 17 X 14 X 40 X 30 X 15 X 20 X 16 X 6" ~ The draft between the feed roller and the doffer — (a) = 1298 X 2-16 X 0-0346 = 97 (h) =^11^^ = 99-04 _ 1 20 X 40 X 26-- _ ^'^ - 14 X 40 X 2} " ^-^ "^ AND COSTS OF YARN 65 Points to be considered when altering the Drafts. — The following should always be borne in mind when deciding the drafts between the various points : — The draft between the lap and the feed rollers should not be more than sufficient to keep the lap straight. If this is exceeded irregularity in the cotton fed will result. Smooth lap rollers are liable to cause slipping of the lap, causing fluctuations, and a greater draft than that estimated. The corrugated and ribbed forms of lap roller eliminate this tendency. The draft between the feed roller and lickerin varies con- siderably. It is customary to alter the speed of the former part whenever a change in the draft is necessitated. That of the latter part is rarely interfered with, being generally about one- half the rate of the cylinder. Altering the draft at this point, therefore, changes the rate at which the fibres are presented to the action of the lickerin, and therefore controls the duration of its combing action upon any given fibre. The draft between the flats and the cylinder is regarded generally as fixed for different classes of cotton. Alterations in this are made by varying the speed of the flats. The rate of movement of the flats in the main governs the duration of the cylinder's action upon a given body of fibres, and also the amount of clean carding surfaces introduced, and hence it is proper to vary their speed according to the exigencies of card- ing. With neppy, dirty, and matted cottons a higher rate of this part is expedient. For low American, Indian, and like qualities of cotton, they are worked at about double the rate in vogue for the clean qualities of American and Egyptian. The draft between the cylinder and doffer is also varied, probably more than is expedient. In this the speed of the doffer is often regarded as subordinate to the count of sliver. The propriety of this is discussed elsewhere. The draft between the dofler and the calender is only varied slightly. It should always be such that the sliver, or " web," does not sag to an extent which is detrimental. On the other hand, if the draft is too much, irregularity through overstretching will result. The draft between the calender and the coiler delivery rollers should be sufiicient to maintain a slight tension at all times. F 66 COTTOJ^ SriNNING CALCULATIONS Conditions controlling the Output of a Card. — General con- ditions. — When circumstances demand an alteration in the quantity of the output, a know'ledge of the limitations of each action are essential in deciding the best manner of procuring the same. This knowledge cannot be gained without intimate association with the work. Assistance of a general character may be afforded, and this is attempted in the following state- ments. Greater the contrasting speeds of the carding parts, longer the fibres are desired to remain in the carding action ; greater the length of the fibres treated, closer the carding surfaces; more numerous the fibres treated the greater the tendency to strain the fibres. The greater the length of the fibres treated the longer the duration of the action of carding by reason of increased difficulty involved in their separation. The more numerous the body of fibres present in the carding influences, beyond a certain limit : the greater the tendency of damage to them by rolling and excessive straining. This occurs whenever the quantity of fibres are in excess of the capacities of the available carding surfaces, and results in some portion of the weight of the flats being borne by the body of fibres instead of by the bend. This tendency increases as the crowding becomes more intense. This becomes apparent through the increased power required to drive the card. Such conditions are more likely to arise in treating long than with short, fibred cotton. Inconsistent increases in the power consumed by these machines, after alterations of this nature, may be regarded as signs of overcrowded carding surfaces and straining of the fibres. Distinct conditions in respect of the actions of the carding imrts. — The functions of the lickerin are to straighten the fibres composing the fringe of the lap, eliminate foreign matter, carry forward the treated fibres to the range of the cylinder's action. The functions of the cylinder are to take the fibres from the lickerin, to carry them into the range of action of the card flats, whereupon the latter arrest those fibres otherwise than straight. AND COSTS OF YARN 67 The action of the cylinder, about this latter portion of the machine, is directly upon those fibres held by the flats, and partially projecting in the carding action. The gradual straight- ening and withdrawal of these, introduces others more or less contiguous to the carding action. In this way the super- abundance of fibres which the flats receive during the earlier period of their action are held in reserve, and gradually brought into the action. As the fibres are gradually separated and straightened, they are carried off by the cylinder. The functions of the flats are to receive foreign bodies, fibres that are entangled as well as those that are not straight — not in line with the direction of the carding movement ; to present such fibres to the range of action of the cylinder for a definite period. The facility of the flats to arrest and detain foreign bodies and to retain and present the fibres requiring carding, depends upon the efficacy of the points, composing those surfaces, and the quantity of these available. Numerous sharp carding points accompanied with reasonable spacing are the active agents in arresting and presenting fibres for disentanglement and the retention of foreign matter and short fibres. A sufficient supply of clean wire points should be con- tinually passing into action. Should this latter be insufficient the imperfectly carded cotton from the lickerin would be carried forward by the action of the cylinder, and in passing the crowded surface of points of the flats, would tend to embed those fibres already engaging the wire. Those fibres, brought forward, which cannot be accommodated byreason of the crowded character of the surfaces, are subjected to the pressure previously referred to, and are thus strained, ruptured, and nepped according to the degree of overcrowding. To guard against the fibres becoming embedded care should be observed to ensure that the proper inclination of the bend in wire is preserved. This is often depressed through the stripping brush being used in an unclean condition, also by its being set too deep. The wire on all surfaces should have a fine keen point, and this should be maintained in as uniform a condition as possible. The Rate of Movement of the Flats.— It would seem that if the G8 COTTON SPINNING CALCULATIONS wire surfaces act as heretofore described, a period very much less than forty minutes would raore than suffice for the selection of all the desirable fibres from those received by the fiat whilst occupying the first position on the bend. Such may be the case, but since the flats when even in their last position arrest fibres— proved by passing a little coloured cotton in with the lap, this making its appearance on the next flat exposed — the best way in deciding the proper speed of flats is to recognize the strips from them as the index. The speed should be adjusted to give the lightest "strip" that will strip satisfactorily. To adjust the percentage of strip by manipulating the front stripping plate is wrong in principle. There is only one correct position for that part, and that is as near the flats and cylinder as practicable. Increasing its distance from the flats causes the detachment of portions of the entangled fibre and impurities selected in the carding action from the flats as they move out of action, and thus polluting the work otherwise accom- plished. In considering the rate of movement of the doffer, its functions as well as the length or the weight must be kept in mind. The function of the doffer is to take the fibres from the cylinder. The more completely this is accomplished the better. Should the cylinder be only partially cleared of the fibres borne upon it, its influence in carding will be interfered with to that extent ; because it reduces the extent of the surface of carding points at liberty to act upon those fibres presented by the lickerin and " flat " surfaces. The aim, therefore, in working the doffer should be to clear the cjdinder as completely as possible, and to ensure this its surface rate should be as high as practicable. This rate cannot be specified only in general terms on account of the wide variations in the working conditions. Light slivers, poor staple, bad laps, poor selvedges, unsatis- factory doffing combs, badly constructed sliver casements, draughty rooms, all tend to restrict the speed at which the doffer can be run. Under favourable conditions 16 revolutions per minute can be attained. The rate of the flats is as high as 3 per minute. AND COSTS OP YARN 09 The rate of cylinders is 170-180 revolutions per minute for low American and like cottons. The rate of cylinders is 160-175 revolutions per minute for Egyptian and American better qualities. The rate of cylinders is 120-160 revolutions per minute for the longer stapled cotton than those enumerated above. Changes in the Total Draft. — These are accomplished by altering any of the following four wheels : Bevel wheels on the dofifer and side shaft and feed roller. Since the side shaft transmits the motion to the feed parts, a driver wheel will influence the rate of the feed in the direct ratio and the draft inversely, whilst a driven wheel will have the inverse effect. It is customary to alter the draft by means of the side shaft wheel, driving that on the feed roller, and hence it is called the draft change wheel. Whenever this is impracticable, on account of the limits in size of wheel applicable, it is customary to alter that on the feed roller to an extent providing a more convenient range of drafts with the wheels available. Occasionally the side shaft and doffer bevels are altered, but usually these are inconveniently fixed for this purpose. ExKuciSE 4. — What changes in eaoh of the wheels formhig the draft gear in Fig. IG would give IGO of a draft, assuming the present draft 120? Workhifj and Ansivers^ Bevel wheel on doffer shaft = ^^ ^^}-~^ = 30 Bevel on side shaft = —f^f— = b^ Side-shaft change wheel = li><J^ ^ jqi J (inconvenient ; IbO - \ too small) Bevel wheel on the feed roller = ^^^ ^^^''^ = IGO i Exercise 5.— What drafts would the following side-shaft change wheel give, respectivel}', assuming the card contains 120 of a draft when that wheel contains 18 teeth : 14, 15, 16, 17, 19, 20, 21, and 22 ? Ans. 154-3, 144, 135, 127, 113-6, 108, 102-8, 08-3, respectively. Exercise 6. — What sizes of side-shaft change wheels would be required to » Usually changed to secure fresh range of drafts for the available iide-shaft chansre wheel 70 COTTON SPINNING CALCULATIONS obtain the following drafts, assuming 14 gave a draft of 120: 112, 105, 99 93-5, 88-5? Ans. 15, 16, 17, 18, 19. Exercise 7. — What size of feed roller wheel would be necessary, assuming that card drafts ranging from 112 to 160 are required with the side-shaft change wheels 14 to 20 inclusive, and a 14 side-shaft change wheel driving a 120 on the feed roller give 120 of a draft? Ans. 160. What drafts would the various sizes of side-shaft change wheels give after making the alteration referred to in the last question ? Anstvers — With the side-shaft change wheel 14 15 16 17 18 19 20 The draft would be . . . 160 149-3 140 131-8 124-4 118 112 Weapping. For measuring sliver and roves a special machine is used, called a ■v\'rapping machine. This is arranged to measure one yard per revolution. In using this instrument care must always he taken to secure the movement of the cotton in a straight line and also at a uniform tension, and at the same time pre- cautions taken against slippage. Five or six yards will be sufficient length, and the sliver tested should be obtained from different parts of the can, and from several of the cards in the "preparation," in order to get precisely the conditions pre- vailing. The cotton, after being measured, should be compactly wound in the form of a ball to obtain accurate weighing. Exercise 8. — What should be the weight in grains per yard of the sliver produced in cards containing the following total drafts respectively: 160, 149*3, 140, 181*8, 124*4, 118, 112, if the loss in the process m each case amounted to 5^ per cent., and the lap fed weighed 4375 grains per yard ? " Ans. 25-8, 27*6, 29-5, 31*4, 33*2, 35, 36*8 respectively. Exercise 9. — AVhat should the sliver weigh, per 5 yards, respectively, with draft change wheels ranging from 15 to 22 inclusive, if 5 yards of the sliver weigh 134 grains with a 14 wheel? Ans. 5 dwts. 23^ grs., 6 dwts. 9 grs., 6 dwts. 19 grs., 8 dwts. 4 grs., 8 dwts. 14 grs., 8 dwts. 23 grs., 9 dwts. 9 grs., 9 dwts. 18 grs. Exercise 10. — What draft change wheel would give slivers weighing 9 dwts. 6 grs., 9 dwts. 20 grs., 10 dwts. 11 grs., 11 dwts. 2 grs., 11 dwts. 17 grs. respectively, per 6 yards, if with a 14 draft change 6 yards of the sliver weighs 203gi-ains? Ans. 15, 16, 17, 18, 19. AND COSTS OF YARN 71 The Names applied to Cotton in its Preparation. The following are terms used to designate the cotton in its different stages of preparation : — Yarn is the completely twisted thread of fihres. Eove, or roving, the band of fibres twisted to bind them sufficiently to resist handling. It is thus described after treat- ment in the slubbing, intermediate, roving, and "Jack" machines. Sliver, is the band of fibres devoid of twist ; at least, it is regarded as such. This term is used when the cotton is in a round state, in the processes, between the carding and slubbing stages. Lap, denotes that the fibres are in a sheet or ribbon, formed in a roll. This is the state at the opener, scutcher, card sliver lap, ribbon lap, and combing machines. The System of "Counting" Cotton in its Various Stages of Pre- paration. — This is adopted to express the length per unit of weight in a concrete and simple form. The basis of the system, used, is that of numerating the units of length contained in one pound, avoirdupois ; the unit of length, used, being one hank. A special length table is used for subdivision of the hank. It is as follows : — 54 inches (1^ yds.) = 1 thread 80 threads (120 yds.) = 1 lea 7 leas (840 yds.) = 1 hank The table of weights are— 24 grs. = 1 dwt. 18j1t dwts. (4371, grs.) = 1 oz. 16 ozs. (7000 grs.) = 1 lb. Note. — The work is very much siraplitied by the adoption of grain weights and pounds. Much vahiable time is lost in calculation when penny- weights and ounces are used. Thus, the count signifies the number of hanks, in length, of the cotton which are required to weigh 1 lb., and therefore — 1 hank (840 yds.) of No. 1 =1 lb. = 7000 grs. 1 lea (1 hank, or ^f^ yds. = 120 yds.) of No. 1 = ^" = 1000 „ 72 COTTON SPINNING CALCULATIONS I lea(T\bank,or^V4''y<^s.= 60yds.)of No. 1 = ^^'= 500 grs. 1 <'-! 540L = BO ") =rJ^"= 250 .. -i- / L 84^ = 12 ^ =L'^-=. 100 10 " \ 70 " 70 " -^"^ " / " rjQ ^^^ >i J- <'-J-^ ^-4ft = fi \ =t}^- — 50 20 " V140 >' 140 >' "J >) 7 5> 240 " 1_ / 1 8 40 — 1 "I — " •— 25. 120 '> \840 " 840 >' ~ -^ 5J ; )) ~ 840 ~ ''^ " The above are the fractions of a hank usually measured when testing the count of the cotton in the various stages of its preparation. In connection with the weight table a difficulty is experienced in remembering that IS^^ dwts. make 1 oz. To remember that 7000 grs. make 1 lb., and that 24 grs. make 1 dwt., also that 16 ozs. make 1 lb., reduces the difficulty experienced in recalling the number of pennyweights per ounce, because the penny- weights may then be reduced to grains and the grains to pounds. If a similar difficulty occurs with the number of grains in an ounce, by noting that 7000 grs. are contained in 1 lb. of 16 ozs., then ^f{]o = 437^, the grains in an ounce. In this way the difficulties so often experienced by beginners are overcome. In order to ascertain the count when the weight of a given length is known, the procedure is to divide the weight into that of a similar length of count No. 1, each expression being reduced to common weight terms. Thus — Examples — For reasons, see page 73. (rt) Required the count when 1 lea = 50 grains — -^t- = 20 v'J }) » >> ^ " 1 X 24 (c) - 437-5 - -i^-^^~ = 2-285 (d) „ „ „ =i]b. =nr7ooo = ^'i^-- (e) „ ,, 1 hank = 437-5 grains = y = 1^ 7000 ~ 24 = 292 7000 100 = 70 1 ~ 840 X n "^ 0-00119 1 X ] 16 0-01 905 840 X : 1 ~ \J \J X U\J\J 1 X 7' 000 0-H47 "840 X 24" • \J iJt: 1 1 - 840 ^ 7000 1 = 8-3 AND COSTS OF YAllN (/) Kequired the count when 1 hank = 24 grains (9) „ „ „ =100 n (/*) „ „ 1 yard = 1 lb. (0 „ „ „ = 437-5 grains (^) „ „ „ =1 Notes on the worhing of the preceding Examples. (a) The weiglit of 1 lea of No. 1 = 7- lb., ov^-p-^ grs. ; thus, the numerator is 1000 and the denominator 50. (h) The numerator is ] of the pennyweights in 1 lb., because it is the weight of 1 lea of No. 1 in pennyweights, the weight expression of the denominator used in this case. mi • 1 i. • 1 i- 1 11 1 X 7000 The pennyweights ui 1 of 1 lb. - - — ^^ These converted to grains = M^iu - iqoo and 1 dwt. in grains = 24 • iQoa — 4.1-7 (r) The numerator here is I of 1 lb. in ounces = ^£', and the denominator 1 ; . 16 ooQf; 7000 1 ..^^ =2-285...; or,-- X 437:5 {(I) The numerator in this case is again } of 1 lb. and the denominator 1 ; .-. } X I = } = 0-142... (e) In this instance the numerator is 1 lb., or IG ozs., and the denominator ^■^r lb. or 1 oz. respectively, and hence the count = — - or ^'- respectively. ic (/) The weight of pounds and ounces can always be more conveniently expressed in grains than in pennyweights, and hence the numerator is reduced to 7000 grs., and the denominator to 24 grs. ; • 2.00(1 (//) One over 840 is the numerator, because it is the weight of yard of No. 1 expressed in pounds, and 1 the denominator. Exercise 11. — What are the counts of— (a) 1 lea = 4 dwts. 4 grs. ? (&) 60 yards = 2 dwts. 2 grs. ? 74 COTTON SPINNING CALCULATIONS (c) 95 yards = 50 grs. ? (d) 21 leas = 125 grs.? (e) 4 leas = 1 dwt. 16 grs.? (/) 1 yard = 1 dwt. 1 gr. ? (g) 5 yards = 7 dwts. 12 grs. ? (h) 1 yard = 12 dwts. ? What should be the weight in grains of — (i) 1 yard of No. 1 ? (j) 1 lea of 40', 3G\ 84^ 79' ? (k) 30 yards of 4' ? (0 60 yards of 10'? (m) 6 yards of 0-2' ? (n) 15 yards of 0-25'? (o) 1 yard, 0-0340, in ounces? Exercise 12. — What would be the count and weight in ounces per yard of the laps fed in cards containing each 120 of a draft if the amount lost in waste is 5 per cent., and the count and weight of the sliver are — Kespective count Kespective weight in grains per yard Ans. Count = 0-002225 Ounces per yard = 9 Exercise 13. — What would be the count of the sliver and its weight in grains per yard if the draft in the card was 152 and the lap weighed 80 ozs. per yard, the loss in waste being 5 per cent. ? Ans. Count =: 0-32 Weight = 27-35 grs. Exercise 14. — What weight of sliver, in grains per yard respectively, would be necessary to enable a card to produce 800 lbs. of sliver per week of 55 working hours with a doffer 126£ inches diameter when run at 16, 15, 14, 13, and 12 revolutions per minute respectively? Ans. 45-5, 48-5, 52, 56, 61-7. Exercise 15. — What would be the count and weight of the sliver, in grains per yard, in cards containing 120 of a draft, if the lap fed averaged 10, 11, 12 13, and 14 ozs. per yard respectively, and the waste in carding was 5^ per cent. ? Ans. 0-242 0-22 0-202 0-86 count. 34-4 37-85 41-3 44-75 weight in grains per yard. Exercise 16. — What should be the weight of the sliver, in grains per yard, produced by a card containing 120 of a draft, if the lap weighs 10 ozs. per yard and the waste extracted is 5 per cent. ? Ans. 34-6 grs. 0-267 0-241 0-192 0.16 d 312 34-6 43-3 52 0-002083 0-0016 0-00133 10 12,^ 15 AND COSTS OF YARN 75 Exercise 17. — What should be the weight of the lap suitable for a card it the loss in waste is 5 per cent., the draft being 120 and the sliver is required to weigh 36 grs. per yard ? Ans. 4547 grs., or 10-38 ozs. Exercise 18. — At what rate, in revolutions per minute, should the doffer in a card be worked in order to produce 400 lbs. of sliver of 34*G grs. per yard in 54 liours' continuous working, if the doiler is 24*75 inches in diameter and the draft between this part and the coiler delivery roller is 1*10 ? Ans. 10"5 revolutions. The Length of Fillit required to Cloth the Cylindrical Surfaces. — In calculating the length of the fillit required, it is necessary to allow one coil extra in addition to that sufficient for holding. Thus, a cylinder 50 inches diameter, 38 inches wide, to be covered with fillit 2 inches in width, would require 4f coils + 1, and the length for holding, say, about 6 feet — /. f ^ X -2^- X ^- feet + 6 feet = 268 feet Doffers 24 inches diameter, 38 inches wide, clothed with 1^ inches fillit, require about 4 feet for holding, and — fl X ^^ X -^^ feet + 4 feet = 130 feet The following is the procedure in forming the spirals, termed " half-lap " and tapered tail ends, respectively. The latter is commenced the width of one staple and increased gradually to the full width in a length equal to the first coil. The former is commenced one-third or one-half the width, and the spiral obtained in one and a half or two coils, the finishing ends terminating in the inverse manner. Example of preparing "Half-lap." — Assuming the fillifc contains six columns in the width, half the width will be convenient for the commencement; maintain this width for half a coil, and then proceed to add a column, on the right-hand side, at points equidistant in the next half coil. In doing this it is necessary to have the commencement of the last row of each column a distance from the first row of the next column of ^ of A of l the circumference of the cylinder. Thus three columns would be added in the latter half of the first coil. Afterwards, com- mencement is on the right hand, the left half of the end of the first coil must be secured to the "jump-end" of the beginning 76 COTTON SriNNTNG CALCULATIONS of the first coil, and the second coil is commenced with the right-hand half. The left-hand portion is prepared for the cut- away portion as follows : Proceed to widen the right half of the second coil by the addition of rows and columns on the left-hand side in the same manner and at the same rate as with the tapered portion of the first coil, but from the commencement of the second coil, thereby obtaining the full width at a point opposite the commencement of the taper in the first coil. This completes the preparation for cutting. When the columns are odd in number, for instance, seven, commence with the width of three columns to extend over 2 of the circumference, and then proceed to make the tapered portion over the remaining i of the first coil, and put in the remaining three columns required to complete the spiral, in the first 2 of the second coil. In the former instance the spiral extends over 1^, coils at each end, and in the latter over If. The tapered tail end — completed in one coil — is defective in that the terminals cannot be sufiiciently tensioned for satis- factory grinding and working. The tapering should always be on the inside and not on the outside, this being the most com- mon method. Extending the taper in half-lap over the whole of the first coil, necessarily extends the taper over the second coil. This would largely reduce the number of wire points over these portions, making wide gaps of absent points. The finishing-oft" preparation is exactly the inverse of the commencement. licmemher that uniformity in the character of the point is dependent upon uniform resilence of the wire, and this support it obtains through the medium of the tension at the foundation. The Slivee Lap ^Machine. Fig. 17 represents some of the principal parts and the gearing in the sliver lap machine. The object of this machine is to prepare a ribbon of fibres of uniform width, weight, and, as far as practicable, with the fibres laid parallel and distributed uniformly. This latter is only partially obtained, and hence the succeeding process. AND COSTS OF YARN 11 The machine consists of parts having the following functions : — 29 72 50 26 33 6*1 64- 12"Dia. 12'Dia. 5 Dia. 5 Dia. l2Dia. 1^Dia. 30 30 73 21 21 16 Dia. I^Dia. - 22, 26 Fig. 17. (a) The feed parts, not shown, for presenting a fixed number of the carded sHvers in uniform tension, alignment, and placed as 78 COTTON SPINNING CALCULATIONS close as practicable. Also means for the detection of missing slivers and stopping the machine. (&) The rollers (1[, X li X ll) for attenuating the above- named slivers to the most beneficial extent, this is generally up to about 2. (c) The calenders (5" X 5") for smoothing and pressing the attenuated ribbon of fibres. (cl) The lap rollers (12" x 12") for winding the continuous ribbon of fibres tightly upon a wood roller. Calculations relating to the Sliver Lap Machine (Pig. 17). — This machine is driven by a strap from a 9-inch drum on a line shaft making 220 revolutions per minute. The calculated revolutions per minute of the various parts are as follows : — Machine shaft ,_ ^^^^ ^- 220x9 (16"-13-29) / - ^"^"^ ^^> °^'' ~~16~ First drawing roller \ _ o , o 220 X 9 X 29 X 21 x 50 X 41 X 33 (64-26-U") I - «^ -, or, 16 x 72 X 21 X 26 X 24 x"64 Second drawing \ _ qq f; 220 X 9 X 21 x_50 X 41 x 33 X 26 roller (22-1^" / " '^'^'^> ^^'' 16 x 21 x 26 X 24 x 64 X 22 84-2x26 or, — 22— Third drawing roller^ _.noo 220 x 9 X 29x21x50 X 41 (24-33-U") / - ^^^ ^' 0^' 16 X 72 X 21 X 26 X 24 First and second] 220x9x29 calenders > = 49'8, or, --. — z^ (50-5"), (72-5") J 1^ ^ 7^ , 220 X 9 X 29 X 21 ^""^ 16^02^^ Lap rollers . „^ ^ , 220 x 9 x 13 (12"-73-30) } = 22 04, or, ^^^^ 220 X 9 X 13x30 16x73x30 Drafts — Between second and \ -, .-, o . 26 x 11" first rollers / - 1 1°, or, 22x1.^" Between third and \ _ ^ 22 x 64 X 1^ " second rollers / — 1 "4, or, 26x33x1}" and AND COSTS OF YAEN 79 Between third and^ _ -, q < 64x1?/ first rollers / - l'-^^, or, ^^ ^ ^y, Between calender \ _ -, ^-, . 24 X 26 x 5" and third roller / " ^'^^^^ °^'' 41 X 50 x V/ Between calender | _-,.n7 . 64 X 24 x 26 X 5'' and first roller / - ^"^ ' ' ^^'' 33x 41 x 50 X IV' Between lap roller! 72x13x12^^ and calender •' ~ ' °^'' 29 X 73 x 5" Between lap roller ^ _ 64 x 24 x 26 X 21 X 72 x 13 X 12" and first roller } " '^'^^' °^' 33 x 41 x 50 x 21 x 29 X 73 X 1 y' Production. — What should the lap weigh in grains per yard if the number of slivers fed are 14, and each weigh 30 grains per yard ? , ,_^ 14 X 30 Ans. 202, or, -^^^^ . What should be the weight of lap produced in pounds per week of 55 hours, no allowances ? ^,^^ 2204 X 55 X 60 X 12 X 22 x 202 Ans. 2182, or, ^^^ 7 X 700~0- What length in hanks per week should be delivered under the conditions given ? 2204 X 55 X 60 X 12 X 22 Ans. 90, or. 840 X 36 X 7 To alter the Production. — To alter the length delivered : Change the speed of the whole by altering the machine pulleys. To alter the weight delivered : This may be done by allow- ing the length to remain unaltered or otherwise ; in the latter case the weight-unit of the lap need not be altered, but in the former it would be necessary. The weight-unit of the lap and of the production may be altered by changing the draft or the weight of the feed. Draft affects the weight in the inverse pro- portion, whilst change in the weight of the feed would act in the direct proportion. Changes in the draft of this machine are not frequent. When necessary they are confined to the alteration in the draft between the first and third drawing rollers. 80 COTTON SPINNING CALCULATIONS Exercises in Changing the Sliveu Lap Machine. Exercise 1.— With the speeds as in the figure (17), what effect would changing the weight of the sliver, from 30 to 36 grains per yard, have upon the laps produced : (a) The weiglit per yard ? (b) The weight produced per unit of time ? (c) The length produced in hanks? Jns. 252 grs. ; 2620 lbs. ; 90 hanks. Exercise 2.— What changes would be necessary if the sliver used was altered from 30 grains to 36 grains per yard, in order that the weight and length units, delivered, be unaffected? Ans. Alter the draft change wheel to increase the draft : : 30 : 36. Exercise 3. — What changes would secure the same weight per unit of time, and at the same time alter the weiglit of the lap ^ ? Ans. Altering the draft -^. Exercise 4. — What would be the weight per yard, and of laps per 10 hours, if each lap measured 280 yards and one minute is lost at the completion of each ? The lap rollers being of the size given in the figure, and make 20 revolutions per minute ; each of the fourteen slivers fed weigh 28 grains per yard, and the draft in the machine is 2-08. The Ribbon Lap Machine. Fig. 18 represents some of the principal parts and the gearing in a ribbon lap machine. The object of the machine is : to prepare from the sliver laps one which has the fibres arranged in the most suitable manner for combing ; to make the ribbon of fibres uniform in thickness, width, and weight throughout, and with all the fibres parallel. This machine consists of parts having the following functions : (a) The feed parts : Lap rollers 3 ins. diameter, and the detector of missing and light laps ; the latter is not shown. (h) The rollers (1] x 11 X li xlJ,) for attenuating the ribbon of fibres to the extent necessary, to lay the fibres parallel, and to make the ribbon the desired weight. (c) The curved folding plate C guides the ribbon, passing from the rollers, on to the folding table D, placing it upon the latter at right angles to the rollers. In the figure only one head is shown. The machine is usually made with six heads, to treat six sliver laps, and hence the rollers are constructed to deal with that number. There are, therefore, six curved folding plates, and the folding table is continued to the left accordingly. (d) The carrier and compressing rollers, 3 ins. diameter, are placed at intervals along the folding plate to move forward the folded ribbons. AND COSTS OF YARN 81 rrt c^ o in ol b ^1 1 in 1 ci cj 82 COTTON SPINNING CALCULATIONS (e) The calender rollers (5" X 5") for smoothing and pressing the ribbons and completely uniting them. (/) The lap rollers (12" X 12") for winding the continuous ribbon of fibres, or lap, tightly upon a wood roller. The machine is driven by a strap from a 9-inch drum on the line shaft which makes 220 revolutions per minute and drives the 16-inch pulleys on the machine shaft. The revolutions per minute of its various parts are as follows : — T. n 1 n /o'/N iQ.r 220x9x72x25x54x30 Feed lap rollers (3 ) = 13*5, or, — :r^ — wt^ — ^-r^r — — - — — ^ ^ ^ ' ' 16x68x100x70x56 The first draw roller \ _ o^ o 220 x 9 X 72 x 2 5 x 54 (37-40-70) I - ^5 d, or, 16 x 68 X 100 x 70 The fourth draw roller. _ ,^, 220 x 9 X 72 (68-25-li") } - ^'^^' ^^'' The carrier and com- \ _ „-, pressing roller (22-3") / ~ '^' ^^' The calenders (21-5") = 44-25, or. The lap rollers (12"-12") = 18-55, or, ) 16 X 68 220 X 9 X 31 X 22 16 X 54 X 22 220 X 9 X 20 X 15 31, 16 X 40 X 21 220 nv X 9 X 20 X 15 X 21 16 X 40 X 21 X 50 Drafts — Between first roller and^ _ ^ ^o "^^ ^ ^ the feed lap roller / " ^'^^' °^*' 37 x~3 Between second roller \ _ ^^ 37 x 1^ and the first roller / " ^''^'^' °^' 30 X 1| Between third roller and \ _ -...q 30 X 40 x li the second roller / - ^''^^' ^^' 37 x 22 X li Between third roller and ) _ ^ qo 40 X li the first roller / - ^'^^' °^'' 22 x l| Between fourth roller and I ^ op 22 x 70 x 100 x Jj the third roller / " ^'^^' ^^> 40 X 54 x 25 xTi Between fourth roller and I _ ^ -in "^^ ^ ^^^ ^ ^l the first roller / - '^'^^> ^^> 54 x 25 X ll Between carrier and the ^ _ . ^ ^ 68 x 31 X 22 x 3 fourth roller | - 1"18, or, 72 x 54 x 22 x 1| Between calender and \ ^ ^.o 22 x 54 X 20 X 15 X 5 carrier roller ) - ^'^^' ^r, 22 x 31 x 40 x 21 X 3 AND COSTS OF YARN 83 Between lap rollers and ■» _ -, ./^-, . 21 x 12 the calenders | ~ ^'^^' °^*' 50 X 5 Between delivery lap rollers and the feed lap rollers = 6*05, . 76 X 70 X 100 X 68 X 20 X 15 X 21 X 12 °^'' 37 X 54 X 25 X 72 X 40 X 21 X 50 X 3 Production. — The weight, per unit of length of the lap made, is controlled by the weight of the laps fed, and by the total draft. Any alteration in the latter items affect the former in the direct and inverse proportions respectively, namely — The heavier the feed, the heavier the lap, and vice versa. The greater the draft, the lighter the lap, and vice versa. The length delivered is only affected by the alteration of speed of the machine shaft. It is customary to regulate the weight of the lap by altering the draft ; but sometimes by altering the weight of the lap fed. The draft can be altered to a very considerable extent with- out influencing the quality of the work. The customary changes are made through : The pinion (54) or the back-roller wheel (70) for the draft ; the machine pulleys (16 inches) for speed. The restrictions in altering the draft and weight of the feed arise from the gross weight of the laps J;hat are required for the combing machines. Example 1. — If this machine has six heads, and the laps fed each weigh at the rate of 202 grains per yard ; what weight of laps in pounds would be produced in 10 hours' uninterrupted working, and what would be the weight of these in grains per yard ? . 202 X 6 f.^^ . 1 -4«s, — -— - — = 200 grains per yard 6-05 ^ ^ •' ^^.. 12 22 10x60x200 „„„ „ 18-55 X 3-^ X y X .QQQ = 333 lbs. EX.UIPLE 2. — What would be the weight of the laps per yard if the draft- change pinion 54 was changed to 3G ? How would this change influence the weight and length produced in ten hours ? Ans. The draft would be altered in the inverse proportion to the change wheels, and hence — 6-05 X 54 _ q.()7 36 84 COTTON SPINNING CALCULATIONS and the weight per yard of the lap produced would become lighter in direct proportion to the change in this wheel, and therefore — 200 X 36 , „„ . , ^2 = 133 grains per j^ard And the weight produced in 10 hours would be affected in the same terms, 54 : 36, the length remaining unaffected. Exercises. 1. The feed consists of six heads, and the weight per yard of the laps is 240 gi-ains, the draft required being 5. What weight of lap, per yard and per 10 hours, should be produced, allowing 2^ per cent, for stoppages ? Also, what draft pinion wheel would be necessary to adapt the machine, other particulars being as per Fig. 18? 2. If the machine was producing laps weighing 240 grains per yard, geared as in Fig. 18, what would be the average weight per yard of the laps fed ? 3. Upon testing the weight of the laps produced, they are found 224 gi-ains per yard instead of 240 grains : what sizes of draft pinion or back-roller wheel would restore the laps produced to their proper weight ? Also, give the pro- portional alteration that this change would make in the weight of laps produced per unit of time. 4. If the draft pinion 54 was changed to 60, what effect would it have upon the drafts between : (a) the first and second ; (6) the second and third ; (c) the third and fourth rollers respectively ? 5. If the weight per yard of the laps produced became 240 grains instead of 200, what would you suspect, and what would you do ? Combing Machines. Fig. 19 represents the gearing in the Nasmith combing machine. The object of this machine is to comb the fibres and reject those that are defective and below a specified length. The cotton for treatment in this machine is prepared from the card sliver, by the sliver and ribbon lap machines, an alternative to these processes being one head of drawing followed by the Derby Doubler. The former is the modern system, and has many advantages over the latter, the chief of these advantages being a reduction in the good fibres wasted. The names of the parts in the figure are as follows : — E, the lap rollers, F, the pawl actuating the lap roller gear. AND COSTS OP YARN 85 CM//" Nr.iK o <N"H — CM CO g "Si ^■^J» 86 COTTON SPINNING CALCULATIONS G, a crank on the oscillating shaft H. HI, the oscillating shaft for operating the feed and the advancing and receding movements of the nippers. J, a lever coupled to the shaft HI at I. K, a crank ; its stud and slide operate the lever J. L, the machine driving shaft. U, a cam on the comh cylinder shaft. T, a quadrant rack lever centred on HI, and actuated by a stud and bowl, the latter projecting into the cam U. E and 30 is the quadrant rack pinion and spindle. 47 is an escapement clutch, the left toothed portion being secured to the spindle E, the right portion being loose upon E, and engaged and disengaged with the left portion to obtain movement of the wheel containing 47 teeth. P, a cam for controlling the clutch Q. V are the detaching rollers connected by a train of wheels, 47, 20, 18, 17, with the clutch. M, the comb cylinder. N, the brush cylinder. 0, the card cylinder. W, the head calender ; there is one for each head. 30, 25, 17, 20, are the " draw-box." The draw-rollers are four in number, to attenuate the combed slivers. Y, the draw-box calender. Z, the coiler delivery rollers, and the coiler and can wheels are shown beneath. The speed of the comb cylinder in this machine ranges from 90 to 100, according to the quality of staple treated. This machine is especially adapted for combing the shorter staples from the equivalent of G. Middlings American and upwards. Another feature of the machine is the wider range of selection in respect of the length of the fibres rejected. With good staples this can be reduced to as low as 12 per cent, without interfering with the thoroughness of the combing. The piecing is accom- plished on a much better principle, and the adjustments are all much simpler than in the machines constructed on the Heilmann system. The production is also considerably greater. The following are the speeds of the various parts and manner 23 X 90 100 X 90 X 24 23 X 20 . 100 X 25 X 1 25 X 32 100 X 4 X 42 X 35 75 X 80 X 47 lOOx 5 X 42 X 35 ^^' 75 X 80 X 47 AND COSTS OF YARN 87 of ascertaining them by calculation when the comb cylinder makes 100 revolutions per minute : — Machine pulley = 391/. : ^-^^^^ Cam shaft = 100 :i^^-^^|^A|B Brush cylinder = 470 : Card cylinder = 3125 Lap Rollers. Assuming the pawls to move \ four teeth per revolution ( = 2*085 of the comb cylinder ) Ditto five teeth ditto = 2-606 Note.— The number of teeth moved bj^ the pawls may be adjusted to give the desired length of feed. This is the medium of altering the draft. There are two pawl levers, one actuating the feed and the other the lap rollers, in a similar manner, but separately driven. Detaching Rollers.— These are actuated through the medium of the quadrant rack and escapement clutch, the movement of the former being communicated to the rollers only when the latter is closed. The quadrant moves up and down seventeen teeth each revolution of the comb cylinder. The clutch escape- ment is open during a period amounting to eight teeth of the upward movement of the quadrant rack. At this point, in the upward movement, the latter makes a pause to enable the escapement clutch to be closed, and then it resumes the upward movement. This has the effect of turning the detaching rollers backward to the extent of nine teeth of the movement of the quadrant rack. The clutch remains closed during the whole of the downward movement, and hence the detaching rollers are moved backward nine teeth and forward seventeen teeth of the quadrant's action. The pinion engaging the quadrant rack con- tains thirty teeth, and therefore makes ^ of a complete oscillation each revolution of the comb cylinder ; s% and Ifj of this move- ment are therefore utilized in turning the rollers backward and 88 COTTON SPINNING CALCULATIONS forward, respectively. Hence, these movements result in the first 9 X 47 17 X 47 detaching roller moving ^ — ^-. backward, and ^ — ^ forward, respectively, per revolution of the comb cylinder. This amounts to the following rates per minute : — Backward, ;^ ^ = 70 "5 revolutions „ ^ 100 X 17 X 47 ,„.,, , ,. Forward, — ^rr -^ = 133^- revolutions oU X Ay) the forward progress per minute amounting to (133^ — 70"5)j"o X 52- = 177"-2. The second detaching roller exceeds the movement of the first as 18 : 17 on account of the gear. These amounts must be regarded as fixed, as adjustments of this gearing are not arranged for. The combing head calenders are 2f inches in diameter, and make 19*947 revolutions per minute — 100 X 48 X 43 X 40 X 16 X 17 X 33 X 20 24 X 40 X 50 X 25 X 43 X 72 X 20 The revolutions per minute of the first draw roller = 58'645— 100 X 48 X 43 X 4 X 1 6 X 17 24 X 40 X 50 X 25 X 30 The revolutions per minute of the second draw roller = 70-374— 100 X 48 X 43 X 40 X 16 X 17 24 X 40 X 50 X 25 X 25 The revolutions per minute of the third draw roller = 110 — 100 X 48 X 43 X 40 X 1 6 24 X 40 X 50 X 25 The revolutions per minute of the fourth draw roller = 277-42— 100 X^ 48 X 43 XjlO 24 X 4'0~xl^l AND COSTS OF YARN 89 The revolutions per minute of the draw-box calender = 126 — 100 X 48 X 43 X 40 X 2 24 X 40 X 31 X 44 The revolutions per minute of the coiler delivery rollers = 179-43— 100 X 48 X 43 X 40 X 70 X 20 X 20 24 X 40 X 55 X 61 X 20 X 20 The revolutions per minute of the coiler = 52-16 ; „ ,, can = 6-94 — 100 X 48 X 43 X 40 X 70 X 20 x 13 X 18 X 18 24 xlOlTSS^X 61 X 20 X 3^"x¥6 X 84 The drafts between the parts in progressive order work out as follows : — (a) Lap and first detaching roller by gear direct. The progressive movement in respect of the detaching roller amounts to 17 - 9 = 8 teeth of the quadrant wheel, or o^^ of the 47 clutch wheel which drives that roller, per revolution of the comb cylinder, and therefore — - „- — 90 = ^^® progressive movement or the amount gained in revolutions of the detaching roller per revolution of the comb cylinder or per nip. The movement of the lap rollers train of wheels is derived from a pawl moving the ratchet wheel, 75, a certain number of teeth each nip ; the extent of this movement can be varied, and is one medium of tensioning the lap. The feed roller is not shown, but it is also worked by a pawl and ratchet, the pawl being operated each nip, and the ratchet wheel is secured upon the feed roller. The movement of the feed roller is adjusted in altering the draft. If the pawl is moved four teeth per nip or revolution of the comb cylinder, the movement of the lap rollers per nip will be the denominator in the succeeding calculations. Hence the draft — 90 COTTON SPINNING CALCULATIONS (a) By gear direct — 8 X 47 X 9 '^ ^ 30x20x10 ^ 8 X 47 X 9 X 75 X 80 X 47 X 4 _ 4 X42X35 ,,, 30X20X10X 4 X42X35~X 11 ~^'^^ 75 X 80 X 47 ^ (b) By calculated surface speeds per minute— The draft between the first and second detaching rollers — ('') = }-f[:| = 1-058 The draft between the second detaching rollers and the combing head calenders — 48x43x40x16x17x83x20 ^ 24 X 40 X 50 X 25 X 43 X 72 X 20 ^ ^ 8 X 47x18 X 9 30x20x17 xlO = 48x43x40 xl6x ITx 33 X 20 X 11x30x20 x 17 x 10 24 X 40 X 50 X 25 X 43 X 72 X 20 X 4 X 8 X 47 X 18 x"9 = 0-916 1 72"4 <'') =187^8= O-^lS The draft between the combing head calenders and the first draw-head roller — (a) = 20X72X43X li _ "^ ^ 20x33x30x21 ~ ^"^^ W ^ 207:35 ^ ^ ^ 172-4 ^ ^ The draft between the first and second draw-head rollers — , , 30X9X8 , ^ (^^ =28^8X9 = ^"'^ n\ 248-82 ^^ ^'^ = 207^5 = ^'^ («) AND COSTS OF YARN 91 The draft between the second and third draw-head rollers — / N 30 X 9 X 8 . _ _ . ^«> = I7x¥x9 = ^'^^' ^^ ~ 248-82 The draft between the thh-d and fourth draw-head rollers — (b) = i^^ = 2-79 ^^^ 389-21 ^ ^^ The draft between the fourth draw-head roller and the subsequent calender — / N 20 X 2| , 1089 . ^^> = 1089 = ^ The draft between the draw-head calender and the coiler delivery rollers — . . _ 44 X 31 X 70 X 20 X 20 x 2 _ ^""^ ~20x55x61x20x20x2i~-^^'^^ (^> = w = '■''' The draft between the lap rollers and the coiler delivery rollers, when the pawl moves 4 teeth per nip — 48 X 43 X 40 X 70 X 20 X 20 . , 24 X 40 X 55 X 61 X 20 X 20 (a) = X2 4 X 42x35 ^„ X2J 75X80X47 ^ 48x43x 40 x70x20x20x 2 X 47x 80x75 24 X 40 X 55 X 61 X 20 X 20 X 2j X 35 X 42 X 4 = 62-58 Draft between the lap and coiler delivery rollers when the pawl moves the feed-ratchet wheel 5 teeth and 8 teeth respectively — («) = "^ = 50-08 92 COTTON SPINNING CALCULATIONS (i) = ^iS? = 31-29 By proportion — By proportion — 36-04 62-58 X 4 5 62-58 X 4 = 50-07 = 31-29 The percentage of waste at this machine is rarely lower than 14 per cent. If 15 per cent, be allowed, and the weight of the laps per yard be each taken as 28 dwts., a machine with 4 heads ... 28 dwts. X 24 grs. X 4 heads ^ 85 would produce a sliver weighmg fi2^^8 lOO when the feed pawl moves 4 teeth per nip = 36-51 grs. per yard. 28 X 24 X 4 And when the feed is actuated 5 teeth per nip, kTvau" ^ 100 ^ 45-62 grs. per yard. Note. — The length fed of lap per nip when the pawl moves 8 teeth would be The latter length would prove in most cases an impracticable amount in this machine. It would make the combing action very severe, throwing a great deal more work on the top comb than it is capable of accomplishing. Another way of adjusting the draft in this machine is by changing the wheel compounded with the feed ratchet wheel ; this may be called the draft change wheel. Altering this wheel will alter the draft in the inverse ratio, because it will reduce the length feed when it is reduced in size. Changes in the weight of the sliver and the output of the machine may be accomplished by — (a) The draft is altered by the wheel coupled with the ratchet wheel, or by increasing the radius of the pawl lever. Note. — This wheel can only be altered to a limited extent, owing to its alter- ing the ratio between the lap and the feed rollers ; unless the pawl lever, operating the latter, is altered at the same time. The lap is liable to be unduly stretched or puckered if this is not done. AND COSTS OF YAEN 93 (b) Altering the weight of the lap. (c) Altering the length delivered by changing the speed of the machine. The production in hanks and pounds per week of a Nasmith machine geared as in the figure and having four heads, the comb cylinder making 100 nips per minute, using laps 28 dwts. per yard, the draft 62*58, 15 per cent, being lost in strips, time lost 10 per cent., engine time 55 hours per week, would be computed as follows : — 55 X 90 X 60 _ (minutes worked per week 100 ~ i less allowances 55 X 90 X 60 X 179-43 X 2" x 22 ^ i inches delivered per week by ^110 7 ~ ^ the coiler delivery rollers 55 X 90 X 60 X 179-43 x 2" x 22 ^ j hanks delivered per week by 100 X 840 X 36 7 1 the coiler delivery rollers = 110-82 Percent. Revs. P.M. Dia. HrB. Mins. [yards delivered by the 90 X 179-4 3 X 2^^ X 22 X 55 X 60 ^ coiler delivery rollers 100 X 36" 7 ( per week, less stoppages Grs. D«t8. Laps. Percent. 24 X 28 X 4 X 85 _ j weight of the sHver in 6258 X 100 ~ I grains per yard Draft. Weight in pounds of the sliver delivered by the machine per week of 55 hours, no allowance 24 X 28 X 4 X 85 X 17943 X 2 X 22 X 55 X 90 X 60 62-58 X 100 X 36 x 7 X 100x7000 = 485-3 The production, in case the feed pawl moved 5 teeth per nip instead of 4, would be — Weight of the sliver per yard when pawl moved 4 teeth — 4 X 28 X 24 85 ^^ „ 62-58 ^ 100 = ^^"^ ^^^^^^ Weight of the sliver per yard when the pawl moves 5 teeth — _ 365 X 5 _ ^^.^ 94 COTTON SPINNING CALCULATIONS Production in pounds per week of 55 hours — 485-3 X 5 ^^^ . ,, = 606*5 lbs. 4 The length delivered after the alteration would be the same, but the length fed would be one quarter more, and therefore the weight delivered would be proportionately increased. The production per week, if the feed pawl moved the lap rollers 8 teeth, would be — 485-3 X 8 lbs. = 970-6 Exercise 1. — Assuming the speed of the comb cylinder 100 revolutions per minute, and the machine puUej's 14 inches in diameter are changed to 12i inches, what would be the speeds of each of the parts of the machine ? Ansiver — Lap rollers with the pawl moving 4 teeth 2-335 ,, ,, „ ,, o'oob First detaching roller, backward . . . 78'96 „ „ „ forward . . . 149-146 Second „ ,, backward. . . 83-0 „ ,, „ forward . . . 157-92 Cam shaft 112 Comb cylinder 112 Machine shaft 4382% Brush cylinder 404*5 Card „ 3-5 Combing head calenders 23-936 First drawing roller 65-082 Second „ 78-818 Third „ 123-29 Fourth „ 310-71 Draw-box calender 141-12 Coiler delivery roller 200-96 Coiler 58-42 Can 7-77 Exercise 2. — What would be the consumption of laps and production of sliver, in hanks and pounds, per 50 hours' uninterrupted working of a Nasmith comber, and the weight of the lap per yard ; also the percentage of the waste extracted, under the folloAving conditions ? — Sliver produced in 1 minute, 1117 grains. Strips ,, ,, 292 grains. AND COSTS OF YARX 95 Weight of the sliver, 40 grains per yard. Number of combing heads, 4. Draft in the machine, 50. Ansiver — Length of lap in hanks = 8*328 Weight of laps in pounds = G24'8 Length of sliver in hanks = 104"1 Weight of sliver in pounds = 499'7 Percentage of waste = 20 Weight of the lap per yard = 649 grains. Exercise 3, — Calculate the amounts of the laps consumed and the sliver produced, in hanks and pounds, if the pawl moved 5 teeth instead of 4, assuming the latter gives 625 lbs. weight of sliver, and the other conditions as given in the answer to the previous question. 625_^x^5^3^^^3^.2^jj^^_,^^^^ ^'^^^ ^ ^ = 10-41 hank of lap 4 The length of the sliver would be unaltered. The weight of the sliver would be • ^ = 624-6 lbs. Exercise 4. — What would be the consumption of laps and the sliver produced, in hanks and pounds, per 50 hours' uninterrupted working in a Nasmith comber ; also, the percentage of the waste made when the conditions are as follows ? — Production in one minute, 1120 grains of sliver ; strips, 280 grains ; weight of one yard of sliver, 40 grains ; number of combing heads, 4 ; draft, 50. Answer — Sliver Laps Hanks per week .... 100 8 Pounds „ .... 480 600 Percentage of the waste, 20 Fig 20 represents the gearing in a single acting combing machine on the Heilmann system. The object of this machine is to comb the fibres and reject those that are defective and below a specified length. The cotton is prepared for this process in the same manner as that for the Nasmith combing machine, the range in the weight of the laps for the Heilmann being from 200 to 400 grains per yard, and for the Nasmith about double that weight. The actions in these two types of combing machines differ, fundamentally, in that the fibres in the Nasmith machine are 96 COTTON SPINNING CALCULATIONS only submitted to once combing, whereas in the Heilmann they are submitted a number of times, their introduction to that action being graduated. The effect of this is that the Heihnann AND COSTS OF YAllN 97 wields greater powers of discrimination in respect of the length and other features of the fibres selected by it. The respective parts are named as given in the figure. The revolutions of the comb cylinder range from 60 to 90 per minute. This is often spoken of in terms of nips instead of revolutions, there being one nip or complete cycle of actions per revolution of the comb cylinder in the single acting type. In the Duplex type the cycle of actions are accomplished in each half revolution of the comb cylinder. The following is the mode of calculating the speeds of the various parts, for this purpose the comb cylinder being assumed to make 80 revolutions per minute : — Eevolutions of machine \ _ on^i o , 80x80 pulley per minute ' ~ - 1 ' °^ ' ^21 Eevolutions of lap rollers! . , 80 x 1 X 18 X 21 X 20 x 30 per minute / - 1 7 /, or, ^ x 38 X 20 X 55 X 49 Eevolutions of feed roller ^ _ 80 x 1 x 18 per minute J ~ *'^^> °^' 5 X 38 Eevolutions of comb head ^ _ . . . - <. . 80x80x 2 x20 calenders per minute } ~ ^^-^^^ or, 80 X 14 x 20 Eevolutions of first roller] 80 X 25 X 14 in the draw-box perl = 23*33, or, ^ .„ minute J ^5X4H Eevolutions of third roller 80 x 25 X 50 x 40 m the draw-box per > = 104-5, or, ^ — -t-z — ^ minute ) Z5 X 45 X d4 Eevolutions of draw-box | _ ^ 80 x 25 x 50 x 40 X 22 calender per minute i - ^i ^> or, ^^ x 45 X 34 x 40 Eevolutions of coiler de- -i _ o-i . « 80 x GO X 22 X 18 livery rollers per minute f ~ ^^ ^> o^"' 59 x 22 X 18 Eevolutions of brush \ 80x34x80 cylinder per minute •' "~ ' °^'' 25^^1 Eevolutions of card cylin-j _ 80 x 1 der per minute / — z 5, or, ^ Drafts — Between lap and feed rollers = 1166, 49 X 55 X 20 X 1 or, 30 X 20 X 21 X 25 H 98 COTTON SPINNING CALCULATIONS Between lap and comb head calenders = 6'45, 49 X 55 X 20 X 38 X 5 X 80 X 2 X 20 X 2f or — — -- ' 30 X 20 X 21 X 18 X 1 X 80 X 14 X 20 X 2^ Between lap and first draw roller = 6*58, 49 X 55 X 20 X 38 X 5 X 25 X 14 X If or 5. ' 30 X 20 X 21 X 18 X 1 X 25 X 48 X 2| Between lap and third draw roller = 29*51, 49 X 55 X 20 X 38 X 5 X 25 X 50 X 40 X 12 or - ' 30 X 20 X 21 X 18 X 1 X 25 X 45 X 34 X 2f Between lap roller and draw-box calender = 32*5, 49 X 55 X 20 X 38 X 5 X 25 X 50 X 40 X 22 X 2| ' 30 X 20 X 21 X 18 X 1 X 26 X 45 X 34 X 40 X 2| Between lap and coiler delivery rollers = 33*4, _ 49 X 55 X 20 X 38 X 5 X 60 X 2 X 22 or, ' 30 X 20 X 21 X 18 X 1 X 59 X 22 X 2f Between first and second draw rollers — Miiil = 1-24 25 X If Between first and third draw rollers — 48x50x40xlf , ,^ — = 4*48 14x45x34xlf Between second and third draw rollers — 25 X 48 X 50 X 40 X If _ q p 31xl4x45x34xlf ~ Between third draw roller and draw-box calender — = 1-1 22x2f 40xlf Between draw-box calender and the coiler delivery rollers- 40 X 34 X 45 X 25 X 60 X 22 X 18 X 2 22 X 40 X 50 X 25'x 59 X 22 X 18 X 2| = 1-025 The movement of the detaching rollers is derived as follows : The quadrant rack is a part of a lever actuated by a bowl pro- jecting from it into a cam. The rising and falling movement AND COSTS OF YAKN 99 of the quadrant rack is about 12 teeth, so that the 14 wheel receives movement equal to |f of a revolution per (nip) revolu- tion of the cam shaft. The cam on the left hand engages and disengages the escapement clutch, and by this means the difference in the extent of the backward and forward rotation of the detaching rollers is obtained. The clutch is open during the first five teeth of the upward movement of the quadrant rack ; after that movement the quadrant rack pauses to allow the clutch to be engaged, and upon the resumption the detaching rollers commence their backward movement — this is a constant amount, and is equal to seven teeth of the rack pinion. The clutch remains engaged during the whole of the downward move- ment of the rack, and therefore the backward and forward move- ments of the detaching roller amount to -^ and 1 1 of a revolution respectively. This difference in the movements is insufficient to provide the necessary overlay for piecing. Further variations are obtained, to any extent within these limits, by deferring the placing of the leather detaching roller upon the fluted segment until the length of those fibres, already within the nip of the detaching roller, project only sufficent for the necessary overlap. It must be noticed that variations in the overlap cannot be obtained by altering the timing of the closure of the clutch cam. The clutch cam can only be satisfactorily closed at the moment that the pause occurs in the upward movement of the quadrant rack. Closure at any other period will result in damage to the clutch. Notes respecting the Permissible Adjustment in the Drafts. — The drafts between the lap and feed rollers, detaching rollers and head calenders, head calenders and first draw rollers, third draw roller and draw-box calender, draw-box calender and the coiler delivery rollers, must always be such that the cotton is in slight tension without straining. The point admitting of variations in the draft is therefore between the feed and detaching rollers. Alterations in this alter the character of the combing, because it is accomplished by introducing the fibres more or less gradually, and hence the number of combing actions which they are subjected to is altered thereby. 100 COTTON SPINNING CALCULATIONS Feeding a considerable length of lap generally results in greater waste ; hence, light laps and low drafts together are not beneficial. Moderately high drafts — provided the fringe of the lap is well held by the nippers and the more numerous combings are not injurious — are conducive to better selection of the fibres. The weight a machine is required to comb always decides the count of the combed sliver. The length of the staple decides the suitable speed. Eesults must always decide the weight of the lap as its state as well as that of the machine differ so much. The waste made ranges from 15 per cent, upwards, according to the state of preparation of the laps, the amount of short fibre which it contains, and the settings. With laps each weighing 240 grains per yard, a machine, containing six combing heads and a total draft of 33"4, the loss in waste being 18 per cent., would make sliver weighing — 240 X 6 82 „„ „ . , - 33.^ ^ 100 "^ ^^^^^ ^^^ ^ The percentage of the waste is always based upon the weight of the feed. The weight of the waste and of the sliver, delivered per unit of time, together, equal the weight of the cotton fed in that time. These machines usually contain six or eight combing heads, and therefore the amount fed is always that number multiplied by the average weight per unit of length of the lap fed, whilst the length delivered exceeds that fed, in one head, in the terms of the total draft. Exercise 1. — The sliver and the waste produced in a given time weigh respective!}' 520 and 130 grains, the waste discharged by the six combing heads weighing 20, 20, 21, 22, 23, and 24 grains. Give the individual and total percentage of the loss at each head. Exercise 2. — The sliver produced by a combing machine having six heads is at the rate of 8 lbs. per head per 10 hours. The total draft is 32, and the waste made in that period weighs 10'2 lbs. What is the percentage of the waste made, the weight in pounds, and the length in yards of the laps consumed ? AND COSTS OF YARN 101 _>. '*< "3 o > O ■*! IC O u c~ "?• CO lO P4 00 CO 00 co" co" 00 » eo ■^ o ^l t- 'S ^ ^ CO CO 1—1 CD CO t> „ a <o C5 CO irT 00 CO o -«1 CO CO '^i ■^ l>l I— 1 T) .S'S 3 f^!^ ■S o g 3 n tv. c>- 0-. o- C5 Cv. o. c^ -g^'SSS CO T^l £«^-9^ 3 utions comb uder inute. o O O O o 1!0 -tl ir>-. -H !>5 >>t. 00 00 X GC GO t^ CO oo 5)^, O <U « O P. ^3 « fe^ lutions ute of ir deli\ rollers diamet "^ •f -^ -* "** '9 lO ic ^ ^ ^ ^ ^ c>-. lb lb lb 03 00 cc CC CO CO 00 00 o c s ^ > — .^ i. ^ag 2. .a 2 '5 ? o 9 iO cq c^-. CW c^ c^ (N ">) do c^ «-H •s « «*►- CO CO CO tJh ^s-as. a> use's si M « lis 00 X cc ^ o o cv- CO O l-H (M c^ CM '^ (M s = 2 o ^ , » . **« ifS o aS^ 00 00 -t< 'tH T+< CV. CV. c^- *'' <- 35 ja g^-s? M Total draft. •^ ■* o O cp o CO CO Cv. o CO CO t t: c^. CO CO 'Tl -^l -+i to . O.S * ill CO o o :d :s ID CO CO CO u fc. J3 e-S-oS 1^12 o •* ■+I 00 CO o O tH o o CO i:<- o- 00 '*< -^ ?^1? (M !>* (M c^ C4 (M Ol ^?. •- tt «^ r^ 1 OJ oo O CO Tt< lO o l> X a O T— 1 102 COTTON SPINNING CALCULATIONS Exercise 12. — If the machine pulleys in the last question, 15 inches in diameter, are changed to 16 inches in diameter, what difference in the weight of combed sliver, waste, and laps would result ? The Drawing Fkame. The object of this process is the elimination of the irregu- larities, found in the weight of the sliver, at this stage. This is accomplished by repeating the process of aggregation and attenuation. In this process there are usually three repetitions, but sometimes two or four are adopted, the former in coarse, and the latter in fine, work. Eepetition of the process should be discontinued when the desired standard of uniformity is attained. The heads are numbered corresponding with the repetitions respectively. Thus a draw frame of three heads means that the cotton is treated to aggregation and attenuation three times, namely: in the first, second, and third heads. It is necessary to test the sliver, preferably at the last head, at frequent and fixed intervals, four times per day at least, so that any deviation from the standard weight may be detected and dealt with. The tests should be recorded along with the precautionary or correc- tive measures taken in instances of variation. In these tests, 5, 6, or 15 yards will be found convenient lengths to wrap. The sliver tested should be taken in a manner ensuring correct representation of the prevailing condition, the best way being to take a little from each delivery, but not off full cans. The weight is liable to frequent variation at this stage ; the cause of this is not always apparent. The variations foreshadow the working qualities of the cotton and irregularities in the treat- ment prior to this stage. When variations are disregarded, more than corresponding differences may be expected in the subsequent processes, and often complications of an involved character arise through these faults being unchecked. During very dry weather the wrappings tend to the heavy side. A sudden change in the atmosphere will sometimes necessitate an alteration of quite a few teeth in the change wheel. Changes in the mixing which result in the cotton differing are similarly liable. Cottons which are softer than usual should AND COSTS OP YARN 103 be kept on the heavy side, and vice versa. It is also advisable to keep the change wheel as large as convenient. By noting at the commencement of new mixings the quantities and character of the new lots of cotton contained in them, the space occupied by the scutcher laps, and the waste made in carding, it is possible to discern features that are likely to develop in the subsequent stages. These, together with the tests of the sliver at the third head of the drawing-frame provide a good index of the subsequent working capacities of the cotton. The cans should be " put up " systematically at the feed of each head, the aim being to obtain like conditions at each delivery. ** Putting up " more than one full can per delivery is detrimental. Fig. 21. Calculations relating to Draw Frames (Fig. 21). — Drafts between the Various Parts. — Lifting roller A and No. 1 draw roller — ^Qxlt _ 1.047 21 X Ij - ^ ^-^^ 104 COTTON SPINKING CALCULATIONS Nos. 1 and 2 draw rollers — 18 X If ^ '^'^ Nos. 2 and 3 draw rollers — MA^J^.ii - 1-925 25 X 16 X If ~ ^ ^^^ Nos. 1 and 3 draw rollers — ^^ ^^ = 2-67 16 X !■• ^' Nop. 3 and 4 draw rollers — 16 X 100 X 100 X 1 47 X 60 X 20 X 11 = 3-12 Nos. 1 and 4 draw rollers- 100 X 100 X 1 | _ 60 X 20 X 1|~ "* No. 4 draw roller and coiler delivery roller E- 22 X 3 48 X If = 1 Lifting roller and coiler delivery rollers, A and E, the total draft — 20 X 100 X 100 X 22 X 3^^ _ o 7^^ 21 X 60 X 20 X 48 X 1 1" ~ "^ There is much difference of opinion in regard to the system of allocating the draft in the draw rollers of drawing frames which gives the best results. The following has proved a good rule, and is in accordance with the working conditions : — Draft between first and second draw rollers : not more than 1*2 ,, second and third V- draft between first and fourth 1-2 „ third and fourth draw rollers : (draft between the second and third rollers)^. Example. — TIuir, if the total draft in the draw rollers = x, and that between AND COSTS OF YAKN 105 the first and second .Xj, that between the second and third x^, and that between third and fourth x-^ {x in the figure = 8'33) — then, cc = ajj X ir2 X x^ since Xj = 1'2 a; 8-33 ,'. «2 X X3 = p^ =: j.^ = 6-95 The draft a'a is, in most makes of these machines, incou- venieut for changing. Changes in this are only necessary when the total draft referred to becomes abnormal. With this draft a?2 regarded as fixed, the defects arising are through the draft Xo, approaching in amount that of x^ ; when the total roller draft is reduced to 4"38, then x^ and x^ are alike. It must not be inferred from the latter statement that a change of the draft between the first and third rollers is advocated whenever the total roller draft is altered. It is only desired to point out the error arising when considerable change is made in the total draft, and the expediency of affording relief by a slight alteration in the draft between the first and third, in order to redistribute the drafts in reasonable proportions. It is necessary also to draw attention to the desirability of using change wheels of moderate size, avoiding small ones. The revolutions of 1 _ 22 X 18 X 42 _ the coiler per minute] " ^^" ^ l6~x"Wx 69 ~ The revolutions ofl _ 22 x 18 x 18 X 10 x 20 the can per minute J "" ^'-"^ ^ 46 X 20 X 34 X 36 X 104 ~ Whenever draw frames are changed from heavy slivers, to the other extreme, the coils are frequently ill-spaced in the can, and vice versa. This may be remedied by remembering that heavy sliver requires more space, and hence higher speeds of the can than light fine slivers. When the sliver is coiled too widespread it is liable to be troublesome through too much tension caused by binding in the can. This may be overcome by slightly increasing the rate 106 COTTON SPINNING CALCULATIONS of the coiler. On the other hand, when the sliver is not fully distributed — indicated by a wide space between it and the can side — the cans cannot contain as much as desirable. This may be overcome by slightly reducing the rate of the coiler. When the unoccupied space in the centre of the can is greater than desired, it is due to the can being "too eccentric" with the coiler. By reducing this, and at the same time the rate of the coiler, this objection may be removed. The quantity of the production in draw frames varies accord- ing to the speed, the system, and the efficiency of the workers. In some mills, as high as 90 per cent, of the production, calcu- lated from the actual speeds, are obtained with slivers as high as 70 grains per yard. The above may be considered practicable under the best con- ditions. This would give the following, per delivery, in a week of 55^ hours : — Revolutions of front roller. Weight of sliver in grains per yard. Hanks per delivery. Pounds per delivery. 320 55 50 55 60 65 70 13719 55 55 823 905 987 1070 1152 Productions for Speeds ranging from 320 vv to 380 Eevolutions pee Minute OF 13-iNCQ Front Roller. Revolutions of front Weight of sliver in Production in pounds per roller per minute. grains per yard. week. 320 70 1152 330 1198 3-10 1234 350 1270 360 1306 370 1337 380 » 1366 In medium fine (50''-80*) counts, the former of the above speeds and productions would be considered ample, and the sliver would range from 50 grains per yard downwards, according to AND COSTS OF YARN 107 quality of the yarn and the quantity of preparation machinery available. Revolutions of front Weight of sliver in Production in pounds per roller per minute. grains per yard. week per delivery. 320 50-0 823 » 47-5 783 » 450 744 42-5 704 400 765 37-5 726 »> 360 687 In fine counts, 80^ upwards, the speeds would range from 280 downwards, and the rollers would be 1^ inches in diameter in three positions instead of If inches, and the slivers down to 24 grains per yard. The productions are — Revolutions of front roller per minute. AVeight of sliver In Production in pounds per grains per yard. week per delivery. 280 X 1^ F.E. 360 330 300 27-0 240 658 603 548 493 438 Calculations relating to the Drafts in the Rollers (Fig. 21, Y). Between — First and second = 7^ ^. =1-2 Second and third = 30 X 24 24 X 30 X 80 X 100 x 20 x 30 x 9 36 X 24 X 60 X 20 X 47 X 38 X 10 = 1-68 Third and fourth = !^ ^ !! ^ ^? = 3*30 30 X 20 X 9 „. , , . ,, 80 X 100 First and fourth = ,^ _ — ^^ 60 X 20 6-6 First and third = 77 80 X 100 X 20 X 30 X 9 60 X 20 X 47 X 38 X 10 = 2-01 108 COTTON SPINXIXG CALCULATIONS Xotcs in respect of this System of Gearing Rollers. (a) That, since P is the customary change wheel for varying the total extent of the attenuation and the weight unit of the sliver produced, any alteration of P or of the back roller wheel disturbs the draft between rollers 2 and 3 only, and if the total draft be altered by this means gradually to 3'968, that between 2 and 3 would be gradually diminished, no attenuation would then take place between those rollers, and if altered to less than that amount contraction instead of attenuation of the sliver must result between those points. (h) The draft between the rollers 3 and 4 would, under the circumstances mentioned in paragraph (a), always be constant, and hence should the wheels be altered to exercise a greater draft than 6'6, the draft between the second and third rollers only would be increased. Thus, in case the total draft was raised to 11'9, the draft between the second and third rollers would then become as much as that between the third and fourth. By this system of gearing the variable draft is placed at a point which is not the best. This also may be said of system X (Fig. 21), with this addition, that there is room for error in calcu- lation by overlooking that the two trains — eight wheels — are involved in the calculation of the total draft. Another feature in these systems of gearing (Y and X) is the backlash due to the increased number of wheels and indirectness of the gear. This is best understood when the effects upon the sliver are considered with the wheels loosely geared or worn. On refer- ence to the gearing it will be seen that 3 will start after 4, and 2 considerably after this, because in the former there are only three or four wheels against eight in the latter. The system of driving the (2) and (3) rollers direct from the back roller as shown in the other figure has many advantages over X and Y. It ensures the variable draft between those rollers having the lightest work to perform, greater facilities for changes and calculations ; occupies less space, simplifies the parts, fewer wheels are required, and permits the use of larger wheels. AND COSTS OF YARN 109 Exercises. — Calculate the drafts in Fig. 21 between — (a) 1 and 2, 2 and 3, 3 and 4, 1 and 3, 1 and 4, 2 and 4, when tlie compound wheel between 1 and 2 is 20 and 30. (b) 1 and 2 when the wheel marked 20 is 21, 22, 23, and 24 respectively. (c) 1 and 4 when the wheel marked 20 is 21, 22, 23, and 24 respectively. (d) 1 and 4 when P is the inclusive sizes from 40 to 60. (e) 2 and 3 when P is the inclusive sizes from 40 to 60. (/) 1 and 4 when the 60 on the roller 2 is 40, 50, 70, 80. (g) What should be the weight, in grains per yard, and count of the sliver delivered, in each of the three types of gearing given, if the number of slivers fed per delivery were in each case six, and each of these weighed at the rate of 48 grains per yard ? (Ji) If the sliver delivered by a machine, geared as in Fig. 21, weighed 54 grains per yard, what should it weigh if the wheel P was successively 40, 45, 50, and 55 respectively ? (i) What would be the production in pounds per delivery per week with P 40, 45, 50, and 55 respectively, if with a 60, P, 1152 lbs. were produced? The Arrangement of the Drafts in the Several Heads consti- tuting the Draw Frame. — The condition which should govern the extent of the total drafts allotted to each head is that each should be so rated as to be continuously working without pro- ducing more or less than is required by the succeeding machine. It is the most common practice to have the same number of deliveries in each head, and also for the front rollers in these to revolve at the same rate. Practice has proved this most expedient. To get the best results under such conditions, arrange the drafts so that the condition contained in the last paragraph may be realized. The variations in the contents of the cans from the cards occasion considerably more loss of time in the first head, through stoppages, taking this at 10, 7, and 7 per cent, respectively in the three heads, and the revolutions of the front roller at 320 per minute and If inches in diameter, the card sliver at 36 grains per yard, and that at the last head at, say, 60 grains per yard. Then the productive capacity of the third head would amount to — 55 hrs. X 60 X 320 X If" 22 60 93 ..^^^ „ ,,. 36^<7000 ^ y ^ T "^ 100 = ^^^^ ^^'' ^''' ^'^'''''^ Hence, the front roller in the second head would require to produce sliver at the same rate per yard, whilst that delivered 110 COTTON SPINNING CALCULATIONS by the first head would require to be heavier to the extent of the difference in the loss of time, and therefore — 60 X 93 ^^ . T — ^r — = 62 grams per yard The draft in the respective heads on the assumption that the doublings are 6, in each case must therefore be In the first head — 36 X 6 draft = 63 91 fi draft = ~ = 3-43 And in the second head — 62 X 6 draft = 60 •. draft = ?^ = 6-2 dO And in the third head — 60 X 6 draft = 60 /. draft = -TTTT = 6 oU Fly Frames. The primary object in fly frames— slubber, intermediate, rover, and jack — is to attenuate the sliver obtained from the drawing frame to the extent necessary to prepare it for the spinning machine. It would be possible to dispense with fly frames if drawing rollers were perfectly adapted for attenuating cotton. Drawing rollers, as at present constructed, cannot attenuate perfectly bodies of fibres varying in length. Cotton cannot be obtained which does not vary in the length of its fibres. In consequence, the relative sequence of the fibres is altered during attenuation in a degree proportionate to those variations and the extent of the attenuation attempted. This means, that a sliver or rove with its fibres uniformly distributed would have its fibres AXD COSTS OF YAKN 111 otherwise arranged. The less the variation in the length of the fibres the greater the draft practicable. Eepetition of these processes is necessitated to admit of doubling and thereby absorption of the irregularities referred to. There is no doubt that doubling of more than two ends would be advantageous. The difficulties connected with pre- senting more than that number are the most likely reason of its not being adopted. The Object of Twisting. — Twisting assists cohesion, and is employed to the extent sufficient to protect the bodies of fibres at these stages. The Direction of Twist and the Range of Usefulness of Twist, — The rule in respect of the direction of the twist, in rove, is <- twist : although there are instances of -> weft twisting. I I The direction of the twist has a slight influence on the spin- ning : a twist rove makes better and stronger yarn when it is twisted finally in the same direction than when this is done reversely. It is undoubtedly the case that roving twisted in the same direction as the ultimate yarn, would secure better results in spinning. The only reason which can be given for this not being practised, in respect of weft and " reverse " yarns, is that it may not be so convenient to produce on account of necessitating the use of the left hand in piecing. It is advan- tageous, in preparing roving for twist yarn in ring frames, to use the maximum, and for weft or reverse yarn the minimum twist, constants. Twist has a beneficial influence, when it is in the same direction as that required in the yarn, and when not used to excess. The reason for many carders preferring the minimum twist is because it enables a greater production, from their point of view, but this is not the case with the spinner. Eoving may contain too little twist without breaking in the creel. Care should always be exercised to avoid twisting to the extent which may bind the fibres in excess, causing them to withstand the subsequent attenuating powers. Twist Constants. — The efficacy of twist varies in the various grades and kinds of cotton ; it is also influenced by the degree 112 COTTON SPINNING CALCULATIONS of uniformity of the length of the fibres and touch of the cotton. The amount of the twist per inch necessary to bind the fibres to the proper extent varies from \/count X 0*8 to \/count X 1'5. Cottons which are long and harsh and lie compactly require least, whilst those which are short and do not lie compactly require most, twist. The following is a table of the normal twist constants. These, when multiplied by the \/counts of the actual rove, will give the twist per inch suitable under most conditions. Slubber. from : 0-8 to : 1-0 from: I'O to: 1-2 from: 1*1 Inter. Rover. 0-9 0-9 M 1-2 1-1 1-2 1-25 1-3 1-2 1-4 1-4 1-5 Sea Island and Egyptian cottons . . < Brazilian, American, and similar cottons < Indian and similar cot'. ons . . . . -j , . ...^ The Gearing in Fly Frames (Fig. 22). — The gearing in fly frames is identical in all the principal makes. It consists of a principal shaft called the frame shaft, and from this all the parts receive their motion. (a) The Rollers. — The front roller is connected with the frame shaft referred to by means of a train consisting of four or five wheels, F, E, D, C, B, named, respectively : the twist, the twist carrier or compound, the top cone, the end of top cone, and the end of the front roller w^heels ; a compound wheel instead of E being necessary when considerable range of twist are necessary. The back and middle rollers are connected with the front in the following manner : a train of four wheels, 28, 90, 40, 56, and named respectively the front roller (F.E.W.), the crown (C.W.), the pinion (P.W.), and the back roller wheels (B.R.W.) ; these comprise the connection to the latter roller, the crown and pinion being compounded. The middle roller is connected with the back through the medium of three wheels, 25, C, 18 ; they are named the back roller (driver), carrier, and middle roller wheels. (h) The Spindles. — The shafts driving these, one only is shown, are connected by a train of three wheels, 33, H, 33, in case of the back line of spindles ; and a fourth wheel on the front shaft gears with that on the shaft driving the back line of spindles. AND COSTS OF YARN 113 These spindle shafts are furnished with skew bevels, 60, and these drive the bevels, 21, on the spindles. The value of this train is fixed. (c) Winding. — The Bobbins are driven from two points upon the frame shaft, T.W. and M, the motion from these two points being brought together at the terminal wheel, 14, in the differ- ential. The bobbin driving shaft (O) is connected with the sleeve wheel of the differential N, by means of four or five wheels V'dia. / I 1 Top Con -nl one t- f pitch 60^^ Ratchet Wheel Bottom C Fig. 22. in case of the front, and three or four, 45, C, 40, in case of the back bobbin shaft. These wheels are known as the swing train. The sleeve N acquires its motion from the two points, receiving a fixed contribution from one, M ; and a variable con- .tribution from A, the other of these two points ; the fixed portion here referred to being contributed by that part of the differential which is fixed to the jack shaft. In some cases that part is a wheel. The variable contribution is received by the differential from the twist wheel, T.W., on the frame shaft, the motion passing through the top and bottom cones, and thence through a 114 COTTON SPINNING CALCULATIONS train consisting of a varying number of wheels, numbered on the figure 36, 36, 46, 50, 46, 106. The fixed contributor is arranged to supply the movement necessary to rotate the bobbins at the same rate as the spindle ; the variable contributor communi- cating only that necessary to obtain winding at the desired tension. By this arrangement, the cones completely control the winding. When they cease to contribute, winding ceases, through the bobbins then assuming the rate of the spindles. The wheels in this latter connection are known by the following names : the bottom cone, change shaft, winding shaft, differ- ential, differential sleeve, swing, bobbin shaft, skew bevels, and bobbin wheels. The Consequences of altering the Value of the Cone Train. — The value of the wheel train, connecting the fixed contributor with the bobbins, should be a constant, and therefore any departure from the above-named conditions will result in imperfect wind- ing. The value of the wheel train connecting the twist wheel with the differential should likewise be constant. The value of the belt connection on the two cones is the medium for pro- viding the acceleration or retardation of the bobbin necessary to obtain the proper winding tension ; this being a plus or minus contributor according to the conditions of winding adopted. The two conditions in respect of winding, referred to, are bobbin lead and flyer lead. In the former of these the winding is occasioned by the excess in the rotation of the bobbin over that of the flyer ; and vice versa in flyer lead. In flyer lead the bobbin must be accelerated to the extent coincident with the proportional change in the size of the bobbin at the commencement of each new layer of coils, but only in respect of that portion of their motion supplied through the medium of the cones. In bobbin lead retardation takes the place of acceleration. The connection of the front roller with the bobbins is, therefore, such that the latter creates a winding rate coinciding with the rate of delivery by former. Any change in the rate of rotation of the front roller obtains a corresponding change in the winding rate. The cone drums are constructed to comply with the require- ments of certain sizes of bobbins, each portion being adapted for a certain size, and that only. Altering the value of this AND COSTS OF YARN 115 train of wheels is most likely to place the cone strap on a wrong part of the cones. There is only one part that will give the fractional change of speed corresponding with the fractional increase that each added layer bears to the size of the surface it is laid upon. If the strap is not on that portion of the cones, then the tension of winding will be inaccurate. ((?) The Spacing of the Coils. — This is obtained by the move- ment of the bobbin, vertically, past the guiding point of the flyer. This raising and lowering movement of the bobbin is derived also from the twist wheel, through the cones, by a con- necting train intercepting the train between the bottom cone and the differential connections, namely, 13, 60, (W), 10, 100, (V), 14, 56, (U), 36, 50, (T), 14, 90, (S), 22. The necessity for this vertical movement being derived from the cones arises through the number of coils wound retarding at a rate inverse to the increasing size of the bobbin. The number of wheels employed in this connection vary somewhat. The reversion in the direc- tion of the vertical movement is obtained by means of E.B., the reversing bevels ; these alternately engage their driving bevel. The wheels in this connection are known by the following names : Top change, top of upright, strike bevel, reversing bevels, reversing bevels shaft, cannon shaft, bottom change shaft, lifting shaft wheels, and lifting racks. Speeds of the Parts in Fly Frames. Subject. Details of calculation (Fig. 22). Revolu- tions per minute. Surface rate in inches per minute. Front roller, B Spindles, P . . Twist per inch Twist constant 350 X 39 X 35 35 X 130 ~ 105 X 1" X 22 7 ~ 350 X 33 X 60 _ 33 X 21 revolutions of spindle per minute inches del. by the F.R. per minute - 330" - ^ "^ twist per inch V count Note. — Count suitable deiJends upon the twist constant used. 105 1000 330" 116 COTTON SPINNING CALCULATIONS Subject. Top coue (0, D) Bottom cone, Y Details of calculation (Fig. 22). Draft between"! the back and I front rollers [ (1st and 3rd) j Bobbin lifting\ shaft, S / Bobbin . . . 350 X 39 _ 35 ~ Assuming the strap on the parts G" top cone and o\" bottom cone — 350 X 3) X 6 _ 35 X 3i ~ Assuming the strap on the parts 3J" diameter top cone and G" diameter bottom cone — 350 X 39 X 3 1 _ 35 X G ~ 56x90 X r_ ,.g 40 X 28 X 1"~ 3 50 X 39 X 6 X 36 X 13 X 10 X 1 4 35 X 3i X 36 X 60 X lOOx 56 36 X 14 _ ^ 50 X 90 ~ Note. — The above is when cone strap is assumed in positions 6" in diameter driver cone and 3J" in diameter driven cone. And when cone strap is in positions, rcspectivclv, SJ", 6" — 350 X 39 X 3J X 36_X 13 x 10 x 14 35x 6 X 36 X GO X 100 x 56 36 X 14 _ ^ 50 X 90 ~ To wind without stretching, assuming the winding circle and bobbin lead — 1|" in diameter 330 If flyer lead — li X + 1000 = 1000 - -, 330 n X f - Maximum size of bobbin that the cones are adapted for — -Its, ^X6 _ 4-25" When the bobbin is the maximum bize, 4J", and bobbin lead — If flyer lead — For calculations of the speeds of the bobbins as per gearing, see p. 127. Revolu- tions per minute. 390 720 211-2 Kaiio 1 :4-5 0-437 Surface rate in incliea per minute. 0-128 1084 916 1024-7 975-3 0-88 330" in excess of flyer pres- ser 330" slower than flyer pressure AND COSTS OF YARN 117 The Change Wheels in the afore-mentioned Trains respectively.— The following are the customary change wheels :— (a) For altering the rate of the rollers relative to the spindles and thereby the twist— twist, compound, and top cone shaft wheels, in the order named. For altering the total draft or the attenuating powers of the rollers— pinion, back roller, crown, and front roller wheels. For altering the drafts between the individual rollers, the small wheels on the back or middle roller. (b) None of the wheels in this train are altered. (c) For altering the tension of winding. This should be done by the ratchet wheel or adjusting the position of the cone strap forks. The practice of changing one of the wheels in this train, connecting the differential, which is generally recognized, is open to serious objections, which are stated in the section dealing with winding, p. 127. 00 For controlling the spacing of the rove upon the bobbin. The lifter change shaft wheel and strike bevel are the usual change points. Alterations in the Draft.— Alterations in the draft are neces- sary when the count, or the weight per unit of length, are not as desired. Also, when a change is made in the feed, and a corresponding change in the delivery is not required. The formula when changing the draft or the counts, is— Present draft X count desired ,^ count of present feed _i draft present count count of distended feed~|i-equired When the weight takes the place of the count, it is necessary to bear in mind that the weight is inverse to the count, and that this necessitates the inversion of the two terms, desired and present, in the above equation. The total roller draft may be altered by changing the size of any of the four wheels in the train connecting the back with the front roller. The pinion wheel is the recognized change wheel, and the back roller wheel is changed when the limits in respect of the former have been reached. When the limits of the two former are exhausted the crown wheel is changed, but this is not often necessary. 118 COTTON SPINNING CALCULATIONS Changes in the count delivered may be made by varying the count of the feed or the draft in the direct proportion. Changes in the count fed may be checked by inverse changes in the draft. Changes in the sizes of the drivers, in the draft train of wheels, obtain inverse changes in the draft and count, and direct changes in the weight per unit of length. Changes in the sizes of driven wheels in the draft train have the inverse effect to the drivers. Alterations in the Draft, how made. — Changes in the draft, or in the count produced, do not affect the extent of the length delivered by the front roller. Such changes always affect the weight of the delivery, per unit of length, in inverse terms. The draft, as contained in the present roller gearing (Fig. 22), is as follows : — 25 X — Between the first and second rollers = -=-^ A = 1*21 6 18 X 1" , ,,,. , 18 X 56 X 90 X I ^„. second and thn-d „ = 25 x 40 x 28 X r = ^ ^^ „ , , ,, . , 56x90 X 1" ... „ first and third „ = 40^28 "xl.^' "" Any change in those wheels would have effects correspond- ing with those noted in respect of the rollers in drawing frames. The count obtained by the above attenuation in the rollers would be 4*5 times finer than the feed. The feed in the slubber generally consists of one end per rove delivered, whilst in the intermediate, rover, and jack it always comprises two ends. Thus, in the case where 0*2 is the count of the feed in a slubber having 4*5 of a draft, 0*2 x 4-5 = 0"9 would be the count delivered. An intermediate with 0*9 4'5 draft, treating slubbing of 0*9 count, would produce -„- ^ ^'5 = 2025 count. A roving frame, with a like draft, using that 2*025 count of intermediate rove, would produce — ^ — X 4*5 = 4*556 count. AND COSTS OF YARN 119 A change in any of the wheels connecting the first or back with the front roller would have the following effect : — If a driver, the count and the draft would be altered in the inverse, and the weight in the direct proportion. If a driven, the count and the draft would be altered in the direct, and the weight in the inverse proportion. Altering the Draft. — The following would be the draft and count with the draft wheels, as stated below, when the other roller gear is as given in Fig. 22 ; the count of the rove fed beinor 2-025. If the pinion was altered to 60 50 45 36 30 Tlie draft would become 3-0 3-6 4-0 5-0 6-0 The count would become 3-03 3-64 4-05 5-05 6-06 If the back-roller wheel was altered to 51 48 42 60 65 70 The draft would become 4-1 3-86 3-37 4-82 5-22 5-62 If the front roller wheel was altered to 26 24 22 20 The draft would become 4-85 5-25 5-73 6-3 If the crown wheel was altered to 130 120 110 100 80 70 The draft would become 6-5 6-0 5-5 5 4 3-5 Note. — The front roller and pinion wheels (28 and 56) are drivers. The crown and back roller wheels (90 and 56) are driven. The ratio of the crown to the front roller wheel. The ratio of the pinion to the back roller wheel. That any pairs of these wheels possessing these ratios will produce the same results. Examples and Exercises in Changikg the Draft. 1 2 2 ? 3 2 "Bo-i: Draft. ? 6 5-5 Draft gear. Diameters of F.R. and Back R. alike. F.R.W. C.W. P.W. B.R.W. 25 25 25 100 100 100 ? 40 ? 50 60 .T. 1. , T^ rx 5x2 ^ 50 100 _ A^ orking 1.— Draft - —^ = ^ ." p^ X ,^^- = 5 Working 2. — Count fed = 50^ W 5X2 5 2j ,„ B.R.W. 100 „ ...B.R.W. = i^-^^^^ = 60 120 COTTON SPINNING CALCULATIONS ^v T o n .IV 1 2 . . - - CO X 100 . _ >\ orkinsr 3. — Count aelivered = - x oo = 5o; — r ^-- = o'5 ° 2 ? X 2o .p.W. = ^^^? = 43-6 55 X 2o 9 10 11 12 5J c rti "^^ .Q S 0} " c *- 'tc = > Draft. 2-775 30 yds. = 125 prrs. 30 yds. = 125 grs. 30 yds. = 135 grs. 30 yds. = 125 grs. 30 yds. = 135 grs. 0-18 0-17 ? 0-2 to = > I ? 6-0 I Ditto I G-0 1 30 yds. = 50 grs. 5-2 I 50 ! ^^ 6 " 5 u G »1 G 1 ? 1 ? 1 0-7G5 1 0-96 Draft gear. Diameters of F.R. and Back R a ike. F.E.W. C.W. P.AV. B.R.W 28 28 28 28 25 25 25 25 90 90 28 90 28 90 „ 5» » » 90 90 100 ? 100 100 40 50 40 i 56 40 I T Eatio ? 40 [ 56 Eatio ? 56 56 60 CO ? ? 50 I 60 56 '. 63 50 1 ? j Change to the latter ' of these conrU- ! tions. From these condi- tions change to the latter. From these condi- tions change to the latter. The following must always be known to enable the gearing to be adapted for the production of any specific count : — (1) The count required. (2) The count of the feed. (3) The characteristics of the cotton. (1) and (2) determine the draft. (1) and (3) determine the twist. The Eate of the Winding and Spacing of the Coils cannot be accurately ascertained by calculation on account of the dissimi- larity in the size of rovings. The winding must be regulated by adjusting the position of the strap on the cones. The rate of the vertical movement of the bobbin rail must be adjusted to space the coils without tendency to override or apertures Generally about six coils of count one can be laid per inch This is useful as a basis in the absence of other data. AND COSTS OF YAEX 121 The twist per inch obtained by the gearing as per Fig. 22 = 3-03 inches. According to data on p. 112, the twisting would be adapted for — (a) If Sea Islands cotton (?^J = O'l (h) If Egyptian cotton (^~f = 9-1 to G-4 (c) If Brazilian cotton f^Y = (3.4 (d) If American cotton (^-^^2^)' = 6-4 to 5-4 (e) If Indian cotton (^~~^f = 47 to 41 Thus five frames employed as above stated with the draft 4-5 : the count of the feed and that in the creel would be respectively — 9'1 («) 475 = 2-02 /. 2-02 X 2 = 404 C 'A ^^^ ¥5 " -^'^'-^ •*• 1"^2 X 2 = 2-84 p • i ^""^ 4^ " ^'^^ •'• 1-^2 X 2 = 2-84 5*4 (d) -- = 1-2 .-. 1-2x2 = 2-4 4*7 (0 4:5 = 104 /. 104 X 2 = 208 4-1 °^' 4:5 = 0-91 .-. 0-91 X 2 = 1-82 A change in the pinion wheel would have the inverse effect upon the counts produced, and would influence the weight per unit of length in the direct proportion. Therefore a 30-draft pinion instead of 40 would produce the following counts, assum- ing the feed as in the above instances :— 30 6-4 X 40 30 6-4 X 40 30 5-4 X 40 30 4-7 X 40 122 COTTOX SPINNING CALCULATIONS («) — on— = 12 1 (c) "-^3^ = 8-5 id) ^^^^ = 7-2 (.) ^- = 6-27 A change in the back roller wheel would have the inverse effect to that of the pinion. Whenever the count is changed, it would become necessary to re-adjust the twist per inch to \/ count X twist constant. The rate of the front roller would need altering in the pro- portion inverse to the twists. Thus, assuming the twist wheel in each of the frames, referred to in the last-mentioned examples, 39, the changes in count would necessitate the following altera- tions in the twist wheel : — T. , s 39 X \/9l For (a) -^ Note. — The twists are in the direct proportion of the square root of the counts, and hence the latter may substitute the former. For (h) 39 X \/6-4 \/8"5 For (c) 39 X \/¥l \/¥5 For (d) 39 X\/r2 \/5^ For (e) 39 X \/4-7 Assuming x the size of the ratchet wheel and y that of the lifter change wheel, the following procedure would obtain x and AND COSTS OF YARX 123 y adapted for the above-named changes : because the size of the rove and yarns of a given class are found to vary inversely as the square root of their counts when other conditions are equal. For (a) \ and ^- ~ ^ ^ v/9-1 \/l21 .,. aj\/8-5 , 2/\/8-5 Note.— ic must contain more teeth, because these wheels are made a standard size by each maker ; they differ in the pitch of their teeth only. «, controls the movement of the cone strap at the completion of each layer on the bobbin. It is this movement that obtains the retardation in the speed, of the bottom cone, necessary to secure perfect tension in winding. The extent of the movement of the cone strap must be in accordance with the proportional increase resulting from each layer laid upon the bobbin. Hence, the number of teeth contained in these wheels must be altered relatively, inverse to the square root of the counts, which sum represents the thickness of the roves wound. y must contain fewer teeth for smaller roves in the direct proportion of their diameter, these are, for the same kind of cotton, relatively inverse to the square root of their counts ; because a smaller rove requires less space, and hence slower speed of the bobbin rail, of which train 2/ is a driver. If it was preferable to alter a driven wheel in that train, then a wheel containing more, instead of less, teeth would be necessary. Exercises ik Miscellaneous Fly Frame Calculations. 1. In a roving frame the twist -wheel has 30 teeth, and drives hy a carrier the wheel in the middle of the top cone shaft, containing 40 teeth. On the end of the latter shaft a 48 gears with one on the front roller containing 130 teeth. The front roller is 1^ inches in diameter. The spindle bevel wheel has 30 teeth, and that driving it has 55 ; a wheel of 40 teeth on this latter shaft is driven from the frame shaft by one of the same size. Find the twist per inch. 2. Ascertain the twist per inch, the twist constant, the production in hanks 124 COTTOX SPINNING CALCULATIONS and ounces per spindle per 10 hours, under the following conditions in a roving frame. Revolutions per minute: spindle, 1150; F.R. 120: diameter, IJ inch; draft, 5, count fed : two ends of 3-5 hank intermediate rove ; loss of time, 8 per cent. 3. A roving frame is required to produce 9-hank rove containing twist equal to vcount X 1'4, and the spindles making 1200 revolutions per minute; the diameter of the front roller is 1} inch. At what rate must the roller be driven? 4. At what rate must the bobbins rotate to obtain good winding during the first layer under the following conditions : Gear from the front roller to the frame shaft, J-jSii^ 11^ that from the frame shaft to the spindles, ^, f]g ; diameters, of front roller, IJ inch, of the bobbin, 1| inch ; revolutions per minute of the frame shaft, 300? 5. A fly frame making a 6-hank rove has the following change wheels : Draft pinion, 42 ; twist, 36 ; ratchet, 40 ; lifter (driver), 26. What sizes of these wheels respectively would be required for a 5-hank ? Ans. 50, 39, 37, 29. 6. The spindles in a slubber making a 0-75-hank rove are observed to rotate 4"5 times per 1 of the front roller, which is 1] inch in diameter : the change wheels are — twist, 40 ; ratchet, 19 ; lifter, 26 ; draft pinion, 42 : and the spindles are known to make 550 revolutions per minule. Ascertain: («) the present twist per inch ; (i) the twist per inch suitable for 0'58-hank, and also the change wheels required ; (c) the rate of production in both cases in hanks and ounces per spindle per 10 hours, assuming 15 per cent, represents the loss of time. Ans. 1-15 ; 1-01, 49, or |f , 32, 63 ; 81, 173 ; 9-93, 358. 7. What lifter wheels would be most suitable in using the same cotton for I'O and for 0'5 hank, if it was known that 6 coils per inch was the most satis- factory spacing for 1 hank and a 28 lifter wheel (driver) gave 7 coils per inch? Ans. 24; 17. 8. What sizes of ratchet wheels would be most suitable in using the same cotton for 1*0 and for 0'5 hank, if it was known that a 14 was most suitable for 0-68 hank? Ans. 17; 12. 9. The spindles in a roving frame producing 7-hank roving make 1120, and the front roller 100, revolutions per minute ; the latter is 1^ inch in diameter. What twist per inch should the rove contain ? Give the twist constant and the hanks produced in 10 hours' uninterrupted working. Ans. 3*17 ; 1*2 ; 7'02. 10. The draft in the rollers of a roving frame is 6 and the intermediate roving is 2*6 hanks, and two of these are doubled : what count of rove will be made ? If the count, ascertained, has to be changed to 6', and the draft wheels and rollers are F.E.W. 20, C.W. 80, P.W. 40, B.E.W. 60; diameters, F.R. IJ inch, B.R. 1^ inch, which of these wheels would you alter, and to what extent ? Ans. 7-8— P.W. to 52. 11. A roving frame is making 7-8 hank-roving with the following wheels: Draft pinion, 40 ; twist wheel, 38 ; ratchet, 46 ; lifter, 28, What wheels would be needed for 6 ? What eftect would these changes have upon the length and weight produced ? Ans. 52, 43, 40, 32 increase in lengtli, 38 to 43 ; increase in weight, 6 to 8-9. AND COSTS OF YARN 125 Exer- ' Cottiin and count. Twist. Roller gear. AVind- iiig. Spacing lifter wheel. Count fed. Twist cise No. b. S OS .o 'a J3 Pi 1 1-3 a- 03 O I* & P. stant. Present Required Present Required Present Required Present Required Present Required Present Required American 4 8 Egyptian 10 12 American 42 3 Indian 2§ „ 2J Egyptian 16 20 Indian 3 303 ? ? 4-5 ? ? ? ? 4-8 p ? ? 39 ■? ? ? ? ? ? ? 36 ? 50 ? 4-5 ? 5 ? ? ? ? ? 5 ? ? 5 45 ? 9 ? ? ? ? ? 60 ? 50 ? 56 ? ? ? ? 9 56 56 60 60 54 54 40 ? 52 ? 33 ? 20 ? 56 9 24 9 14 ? 14 17 ? ? ? 18 ? 56 ? 42 ? 56 56 48 ? 42 ? 2-84 55 ? 5 1-4 5» 1-0 ? 1-4 »> 1-28 I'l ? 1-3 r4 55 ? ? 1-4 1-5 Winding in Fly Frames is obtained by the Bobbin. — Winding in these frames is clue to the bobbin rotating at a slower or quicker rate than the spindles. In the former case the " flyer leads " and in the latter the " bobbin leads." The rates of rotation of the spindles and rollers being constant, winding is obtained by that of the bobbin differing from the former of these to an extent sufficient to wind the amount delivered by the rollers. Generally, the range in the size of the bobbins is from 1-^- inch upward, empty, to below 6 inches when full. It is not often that full bobbins exceed more than four times their size when empty. Winding is arrested, in these machines, when the bobbins assume the same rate of rotation as the spindle or flyer. Thus if the latter exceeds the former, or vice versa, the difference represents the coils wound. However large the bobbin becomes — when winding is required — the rate of rotation must, as its size develops, approach that of the spindle, but never attain the same speed equal to it. Therefore, if the bobbin leads and the spindle makes 1000 revolutions per minute, however large the bobbin may become, its rate must be something more than 1000. In the case of the bobbin being 1^ inches in diameter, empty, and 6 inches diameter when full, and the length wound equal to 120 times the circumference of the former size, then the bobbin 126 COTTON SPINNING CALCULATIONS must revolve at the rate of 1000 + 120 j< 1.^ 6 = 1030 revolutions when full, as against 1000 + 120 empty. The Use of Cone Drums. — Cone drums are used to give the necessary variations in the speed of the bobbins. Their work consists of contributing toward the driving of the bobbin an amount sujBicient only to ensure winding at the desired tension, the remainder an amount which is always equal to the rate of the spindle being obtained from a fixed contributor. The Use of Differentials. — Differentials admit of the trans- mission of the motion from the two above-named sources with the most satisfactory results. A simple way of calculating the motion transmitted through the differential gear is as follows : — Let n denote the motion issuing from it ; m, that portion of n derived from the fixed contributor ; a, that portion of n derived from the variable contributor; M and A, the rates of those parts of the differential responsible for m and a Fig. 23. respectively ; t, the values of the respective connecting trains connecting M and A with n — then n consists of ??i ± a Applying this to the Holdsworth differential gear (Fig. 23) : — When M is at rest and motion is imparted to A, revolutions oi n = k ± Kt (in the same direction). AND COSTS OF YARN 127 When A is at rest and M is moved, then — revolutions of w = Mt in the opposite direction to M. Therefore when A and M rotate in the same direction, revohitions of n = K ± A.t ~ Mt and when A and M revolve in opposite directions, revolutions oi 71 = A ± At + Mt Thus, if M makes 300 and A 60 revolutions, both in the same direction, and the value of i is 1, then, by using n = a — m, or its equivalent, n = A + kt — M — M = 60 + 60 X 1 - 300 X 1 = 120 - 300 = - 180 revolutions .'. )i = 180 revolutions in the direction opposite to A Should A and M move in opposite directions at the rates of 60 and 300 revolutions respectively, then — )i = a + m or, n = A + At-\- M? .-. 7t = 60 + 60 X 1 + 300 X 1 = 420 in the same direction as A Thus, the fractional movement of n, due to a, is, in the latter instance, 120, and that due to m is 300, so that the plus 60 has become plus 120, and the minus 300 has changed to plus that sum. Examples in Calculating the Length Wound upon the Bobbin with the Principal Types of Differentials. The particulars contained in Fig. 23 are those existing in a roving frame in working condition. The particulars not given in the figure are — The diameter of top cone, in the part on which the centre of the cone strap rests, is b\\ inches, and the diameter of the bottom cone, also opposite the centre of the strap, 3/g inches; the diameters of the empty bobbin 1^^"^,; inch, and that of the front roller 1]- inch. Under these conditions the revolutions of the spindle per mhiute = r- = 11425 ^ ^ 33 X 21 ^ 128 COTTON SPINNING CALCULATIONS and the revolutions of the bobbin per minute, when the bottom C3ne is stopped, or when the twist wheel is — 40 X 21 Since the two wheels in the sun wheel are carriers, and the wheel on the frame shaft driving them is 36 and that driven by this train is also a 36, t therefore equals H}; = 1. Hence the revolu- 40 X 60 tions of the bobbin per minute = 400 X 1 X = 1142f or the same speed and in the same direction as the spindle. The revolutions of the bobbin per minute, when the bottom cone is working and the twist wheel is 50, are ., , A. -4- Tir.N^O X 60 or — r-/ 400 X 50 X 91 X 2 3 X 19 400x50x91x 23 X 19 V .^ 1 LV 1 X35x55xr20xl30"^ 1 X35 x55 X 120x 130 /" J 40 X 60 ^ 40 X 21 Here ^ = 1, and the sun wheel moves in the opposite direction to M, and, therefore, the sign is +, hence /o w 400 X 50 X 91 X 23 X 19 , ,^^\ 40 x_60 V 1 X 35 X 55 X 120 X 120 / 40 X 21 = revolutions of bobbin per minute = (57 X ^ + 400) X ^^ = 1306-8 Therefore, the revolutions of the bobbins in excess of the spindles = 13068 - 1142-8 = 164 The length of rove wound upon the bobbin per minute, neglecting the facts that the rove is wound spirally, and also that the actual winding radius is greater than the radius of the bare bobbin, is = 164 X r- = 612 inches per minute lb X 7 AND COSTS OF YARN 129 the revolutions per minute of the front roller being — ^^ — ^t^ — > ^ *= 35x130 and the length delivered by it in that time — 400 X 50 X 35 X 5" X 22 ^^^ . , = 1 X 35 X 130 X 4 X 7 = ^^^ ^^'^"' Upon this basis the bobbin is shown to wind 7 inches more than the actual length delivered by the front roller. When the amount due to contraction in the roving, by reason of the twist inserted in it, is added to the difference due to the spiral dis- posal of the coils, and also to the difference between the actual radius of these coils and that of the bobbin, the tension of winding must be considerably more than is represented in the calculation. The particulars contained in Fig. 24 are of a roving frame. 30 9,0 14 308 revs. 25 >,ni^^1R pei^^min. Fig. 24. the differential in this instance being of the Curtis and Ehodes type. Proceeding to deal as with Fig. 23 — n = m ± a When M is at rest it will be seen, upon examination of this differential, that, if the bottom cone is rotated, n = a, or Kt and in the same direction. 130 COTTON SPINNING CALCULATIONS When A is at rest and M is rotated, n = 111, or M — M^ and when M and A revolve in the same direction, 11 = m + a, or M - Mi + At Therefore when M and A revolve in opposite directions, n = m - a, or M - lit — kt The value of t in each of the above instances is the same, being — 30 X 18 X 14 25 X 30 X 90 According to the particulars contained in the figure, it mil be seen that when A is at rest, n = 308 - S08t 308 X 30 X 18 X 14 n = 308 - 25 X 30 X 90 The portion of n denoted by a, when the diameters of the cones at the points opposite the centre of the strap are — top, 5|, bottom 3^ inches ; equals 308 X 39 X 5f X 36 X 46 X 46 x 30 X 18 X 14 35 X 3i X 36 X 50 X 106 X 25 X 30 X 90 M and A are indicated in the figure as working in the same direction, the flyer and the bobbin are also revolving in the same direction, the latter leading ; the connecting sign between m and a must therefore be plus — .-. It = (3O8 - 308 X 30 X 18 X 14^ 25 X 30 X 90/ / 308 X 39 X 5| X 36 X 46 X 46 x 35 x 18 x 14\ \ 35 X 31 X 36 x 50 X 106 X 25 X 30 X 90/ Under these conditions the revolutions of the bobbin per minute will equal — 4 5 X 60 " ^ 40 X 21 AND COSTS OF YARX 131 or — F/^QAQ 308 X 30 X 18 X U\ Li^aOS 25 X 30 x~90/ 4- 25 X 30 X 90^ /3 08 X 39 X 5| X 36 X 46 X 40 x 35 x 18 X 14 \ 35 X 3i X 36 X 50 X 106 X 25 x"W X 90 )] 45 X 60 ^40X21 = ^^^^^ Of this sum the exact amount due to the cones, signified by a, is — /308 X 39 X 5| X 36 X 4 6 X 46 X 35 X 18 X 14 \ 45 X 60 V 35 X 34 X 36 X 50 x 106 x 25 x 30 x 90/ ^ 40 x 21 = 87'27 revolutions per minute The amount contributed directly from the shaft through the differential, and signified by m, is — / 308 308 X 30 X 18 X 14\ . . 45 X 60 = 8791 \ 1 25 X 30 X 90/ 40 X 21 The revolutions which the spindles would make per minute are = 308 X ^^ = 880 in the same direction as the bobbin. Thus, the bobbin leads the flyer to the extent of 966-37 - 880 = 86-37 revs. This represents the amount of rove wound, which should of course be approximately equal to that delivered by the rollers. The revolutions of the front roller in the same time are Therefore the length delivered per minute is = 92-4 x22 = 290-4 The amount which the bobbin would wind, assuming the material wound was | inch radius from the centre of the bobbin, equals 86-37 X li X V = 339-71 inches 132 COTTON SPIXXIXG CALCULATIONS Under these conditions the 290*4 inches of rove delivered by the front roller per minute would be stretched to 339'71, or to the extent of 839-71 - 2904 = 49 31 this being 17 per cent. A noticeable feature in respect of the gearing in this figure is that the bobbin is not driven at the same rate as the spindle "uhen the cone drum ceases to bo a contributor. This makes the correct adjustment of -winding impossible. Thus, when the cone is stopped, the revolution of the bobbin per one of the spindle is — 21 X 33" / 21 X 33 X 30 X 18 X 14 60 X 33 X 25 X 30 X 90 r 21 X 3^ _ / Uo X "33 \ )] 45 X 60 40 X 21 = r^i - "^^ 1 45 X 60 26250 - 2940 . 45 X 60 Uo 1250 J ^ -60 1250J '^ 40 X 21 23310 X 45 X 60 999 75000 ^ 40 X 21 = 0-999 75000 X 40 X 21 1000 The bobbin moving slower to the extent of O'OOl per revolution of the spindle, and thus, whilst the cone is stopped, if the spindle makes 880 revolutions, the bobbin would make 880 X 0-999 = 879-12 revolutions T.W.46 256 revs, p er, min. '" ^'^,414850 40 Ftg. 25. The particulars given in Fig. 25 are taken from an AND COSTS OF YARN 133 intermediate frame. The differential in this case is of the Tweedale type. Dealing with this as with the previous ex- amples — n = m ± a When M is at rest and the bottom cone is actuated, n = a, or At and in the same direction. When A is at rest, 71 = OT, or M — M^ When M and A revolve in the same direction, n = m + a, or M -Mt + At When M and A revolve in opposite directions, n = ??t — a, or M. - Mt - At The value of t in this case is — 18 X 16 80 X 48 Taking the speed of the frame shaft at 256| revolutions per minute with the bottom cone at rest — n - 2562 _ 256|_x 18 x^e '' - "^""^^ 30 X 48 This being the portion contributed to n, from source m, when M and A are both in action together. That portion of n contributed from source a, when the dia- meters of the top and bottom cones — at the points opposite the centre of the strap during the winding of the first layer — are 5^ inches and 3| inches respectively, will be — 2562 46 X 57 X 18 X 44 X 18 X 16 '^ ^ 48 X 3| X 68 X 84 X 30 X 48 therefore when the M and A are working together — / 256| X 18 X 16\ / , 46 x Sj X 18 X 44 x 18 x 1 6\ n-[Zob,, 30^^/ + V^^-' ^ 48x3^x68x34x30x48^ the revolutions of the bobbins being — 50^^ '' ^ 42 X 30 134 COTTON SPINNING CALCULATIONS The revolutions of the bobbin per minute are therefore— r(o^a2 256§ X 18 X 16 \ f ^ 46 X 5| X 18 X 44 X 18 X 1 6^-| 50 X 55 P/o/rfl.A ^1 o\ 1 OT ol 50 X 55 = (205-3 + 27-3) X f^^^ = 508 The revolutions per minute which the bobbins would make if the bottom cone was stopped would be — (256-6 - 51-3) X ^2-^0 = ^^^'^^^ The revolutions of the spindles per minute would be — The revolution of the bobbin per 1 revolution of the spindle, according to the above working, is therefore — 448148 ^ ^ 448-148 ~ Working directly from the spindle to the bobbin, this last result is proved as follows : — [- 30 X 42 _ / 30 X 42 X 18 X 16 \-i 50 x 55 L55 X 40 V55 X 40 X 30 X 48/J ^ 42 X 30 = revolutions of bobbin per 1 of spindle _ r315^ 63 1 50 X 55 _ 252 x 50 X 55 ~ L55O - 550J ^ 42 X 30 ~ 550 X 42 X 36 = } = 1 revolution of bobbin per 1 of spindle The revolutions per minute of the front roller are — 2562 ^ 46 X 48 ^'^ ^ 48 X 130 The length of rove delivered by the front roller per minute — orA2 ^ 46 X 48 X 1" X 22 __^ . . 2564 X -J7Z zr^rx z =- = 285 inches ^ 48 X 130 X 1 X 7 AND COSTS OF YARN 135 The number of coils of rove wound per minute, being the difference in the revolutions as compared with the spindle — = 508 - 448-i48 = 59-85 nearly The length actually wound on the bobbin, assuming the radius of the coils ~, 1-^ inches being the diameter of the bare bobbin, would be — = 59-85 X i-— ^^^ = 305-6 inches 8x7 Thus the length of the rove wound on the bobbin exceeds that delivered by the roller to the extent of 305-6-285, or 20-6 inches, equal to 7*2 per cent. Fig. 2G. In Fig. 26 the differential is that known as the Fallows motion. The particulars herewith given are of a slubbing frame. This differential differs considerably from the usual types, and an explanation of its action is deemed advisable. The right extreme of the portion marked A consists of a cam, the face of this bears against the side of a disc formed upon the rim of a double wheel. Wi and W2 denote the left and right- hand sides of this disc wheel. The teeth are of special design, and the wheel is mounted, loose, on a spherical bearing. This spherical bearing is secured to the driving shaft. This form of bearing admits of a portion of Wi being in gear at a point with M, and a portion of W2 also in gear at a point with N, but on the opposite side of the axis. Thus, the double wheel gears and 136 COTTON SPINNING CALCULATIONS worbs in an oblique position, and this is maintained by the pressure of the cam against the sides of the disc. Under these conditions Wi and W2 act as a compound wheel toward motion passing from M to N. Under these conditions the value of the train would be — = K ^ Wi ^ N The effect of the movement of A, when M is at rest, is that the cam would compel the gearing points of Wi and W2 to circu- late, the teeth of the former entering and emerging from the teeth contained in M as A revolves ; therefore if Wi contains the same number of teeth as M, no circumferential motion of Wi or W2 could accrue. This reasoning applies in a similar manner to W2 and N. Should M and Wi contain different numbers of teeth, then circumferential motion will be imparted to Wi and W2 in the direction opposite to that of A, when Wi contains less, and in the same direction when Wi has more, teeth than Wg. Thus, the movement of Wi would be Wi — M, in teeth per revolution of A, and its rotary movement would be — Wi - II Wi The movement in teeth made by W2, in the same time, would be— W i - M W2 Wi ^ 1 and, therefore, if N contained the same number of teeth as W2, the movement of N would be the same as W2. If the number of teeth in W2 and N were not alike, the movement would be further affected by reason of the cam A causing all the teeth in W2 to enter, and emerge from, as many of those in N as are contained in W2. Thus, the action in this case must be, when M is at rest and A makes one revolution — = ^Vi- M W2 N - W2 Wi" ^ N "^ N In this differential t has two values. In respect of the motion from M its value is — M W2 W ^ N AND COSTS OF YARN 137 Let this be termed ti. "When the motion is from A its value is — Wi - M W2 , N - W2 Wi N ^ N Let this latter be denoted by fa- it will now be possible to proceed to deal with this in the same manner as with previous examples — n = 111 ± a under all conditions. Therefore when A is at rest — n = M^i in the same direction. When M is at rest — n = Af2 the resultant direction depending on the differences in the number of teeth contained in the wheels M, Wi, W2, and N. This will be indicated by the sign being either plus or minus. When M and A revolve in the same direction together— n = Mti + A?2 Taking the particulars of the gear as contained in Fig. 26, and the diameters of the cones at the j)oints opposite the middle of the cone strap, when the first layer is being wound, as follows : — top 11 inches, bottom 3;| inches, and that of the bare bobbin li inch; then: the revolutions of the bobbin per minute when the twist wheel is 0, or when the bottom cone is not engaged, would be, according to the formula — 165 X 3-2 X 36 X 63 X 50 ^r^n onn 1 X 3b X 36 X 58 X 2b The revolution of the bobbin per minute with a 50 twist wheel, assuming M to be at rest whilst A is in motion — _ rl 65x46x7^x26x80 . 36-3 2 36 36-36 H 63^50 ~ L 1 x24x3|jx75x50V 36^^36"^ 36 Jj ^ 58 x'26 _ 165 X 46 X 57 X 26 X 8 X 4 x 63 x 50 _ ~ 1 X 24 X 27 X 75 X 5 X 36 X 58 X 26 ~ Therefore the revolutions per minute of the bobbin during the winding of the first layer would be — = 306-366 + 85-95 = 392-316 138 COTTOX SPINNIXG CALCULATIONS or — 1- 165 X 32 X 36 /165 x 46 x 7^ X 26 x SO V 36 - 32 36 36-36 \-i L 1 x36x36'^V 1 x24x3tx75x50A 36 ^36^ 36 /J x|^^-^? = 392-316 58 X 2o The revolutions of the spindle per minute are — ^f '"'.I'^f. = 306-306 1 X 58 X 2o The number of coils of rove \Y0und upon the bobbin per minute are therefore — = 392-316 - 306-366 = 85*95 The following will therefore represent the length of rove wound : — 1- X 22 85-95 X -^-= — = 405-193 inches per minute The front roller, in that time, makes — 165 X 46 X 40 , ,. fr. T-, r- revolutions 24 X 115 or delivers — 165 X 46 X 40 X It X 22 ^^_ noo • i, ^, ^^^ ^ = 388-928 mches of rove 24 X Ho X 7 Therefore that length is stretched, if the rove is assumed to have no thickness, to 405-193 inches, or to the extent of 13-265 inches more than the rollers deliver; this is equal to nearly 4| per cent. The particulars contained in Fig. 27 are those of a slubber frame, the differential being that known as Brooks and Shaw's. The action of this differential is readily understood. Applying the formula as in the previous examples — n = m ± a for all conditions of working, the revolutions which the bobbin would make per minute, if the bottom cone was stopped, or if the twist wheel was 0, are — , ^ , 74 X 50 = ^" ± '^ ^ 5^^4 AND COSTS OF YAEN 139 Here — [0±( -( m = Mt a = k — At _ 30 X 18 ^ ~ 18 X 37 M = 200, and A = 200 X 46 X 6|il X 30 X 20 X 56n X 32 X 3^ X 41 X 40 X 64. 200 X 46 X 6f ji X 30 X 20 X 56 X 30 X 18 X 41 X 40x64x18x37 32x3i )] 74x50 ,^^^ X =7, — ^, = 100-5 52 X 24 The sign ± in the last instance is determined by the directions of M and A ; when they move in the same direction it is + , and when opposite it is — . Fig. 27. The revolutions of the bobbin per minute, when the cone strap is in the initial position and M and A are in motion, as per conditions in the figure, may be ascertained by adding the speed under the two sets of conditions together, i.e. — 480-77 4- 100-5 = 581-27 obtained as follows : — r200 X 30 X 18 ^ /200j< 46 x 61-1 x 30 x 20 x^6^ 18 X 37 32 X 3i X 41 X 40 X 64. _ 1^2 00 X 46 X 6|i^ X 30 X 20 X 56 x 30 x 18 \-i . 74 x 50 32 X U X 41 X 40 X 64 X 18 X 37/ 52 X 24 140 COTTOX SPIXXIXG CALCULATIONS therefore, of these the bobbin -^ould make — /200 X 30 X 18\. ^\ 74x50 ,^^,f, , , . ' . , ( -^i T7^ — 7^ ± ) X -^c — 277 = 480] y revolutions per minute V 1 X 18 X 37 ^ £)2 X 24 ^ " ^ Calculating directly from the spindle to the bobbin, the revolu- tions of the latter per one of the former would be — /24 X 52 X 30 X 18 ^ ^\ 74 X 50 , ± X -^ ^ = 1 \50 X 60 X 18 X 37 ~ / 52 x 24 The revolutions of the bobbin, assuming the bottom cone to rotate whilst M is at rest and the diameters of the top and bottom cones, at points opposite the centre of the cone strap whilst in the initial positioji, being G\\\ inches and 3i inches respectively, would be — = [162-162 + (179-177 - 145-278)] x 14^^ = (162-162 + 33-899) x L^ T: = 581-27 The rate at which the coils are wound during the first layer laid upon the bobbin is therefore — 581-27 - 480-77 = 100-5 per minute The rate at which the rove is wound — 100-5 X 1^ X '--- = 473-78 inches per minute The rate at which the front roller revolves — 46 X 65 200 X q5 :r^ revolutions per minute = 1431 oA X -LoU The length delivered per minute by the front roller is — „„„ 46 X 65 lyV X 22 ,„^^. , 200 X ^ -^ X -^^ = 480-0 inches oZ X ioU / The amount of rove which the bobbin winds in excess of that delivered by the front roller, assuming the radius of the winding circle of the rove f inch — = 480 - 473-78 = 6*22 inches or 1-3 per cent, less than that delivered. The Speed in Fly Frames. — The speed at which the most satisfactory results are obtained var}- with the working AND COSTS OF YAllN 141 conditions : the kind of work, the efficiency of the machines, skill and organization of the operatives. Data on this suhject should not be regarded as inflexible, but should be subjected to modification such as experience and developments, in the application, suggest. The rates of spindle speeds attainable in modern makes of these frames, fitted with long collars, are — Kind of cotton. Slubber. Intermediate. Rover. Jack. Egyi)tiau 450-50U G50-800 950-1050 1 000-11. jQ American 550-700 700-850 1050-1200 Indian tJOO-700 750-850 10.50-1200 Adopt the highest beneficial speed and fix other conditions so that the whole of the machinery is continuously occupied in producing the required amount. Proportions of Machinery in the Carding Department. — The fly- frame processes usually consist of three stages, but sometimes two and four are adopted. They are named respectively : slubber, intermediate, rover ; slubber, rover ; slubber, intermediate, rover, jack. The number of these processes expedient depends upon the extent of the attenuation desired prior to spinning, and also, to some extent, upon the character of the cotton. Uniform stapled cottons are influenced less detrimentally^ by high drafts. Bej^ond a certain count the roving can be more economically prepared by an additional process. That limit cannot be fixed. It ranges upwards from between 15 and 20. The draft necessary to attenuate the drawing sliver to the desired extent for sj^inning is distributed amongst these two, three, or four processes in certain proportion (see p. 142). In the machinery from the card onward to spinning it is customary to arrange the machinery in what are termed " pre- parations." A "preparation" consists of one slubber and all the other machinery necessary to prepare as well as to deal with its product. Such may be literally expressed as a slubber 142 COTTON SPINNIXG CALCULATIONS and its complement. The following are the proportions of the machinery forming one preparation in — Cards. Combers. 1 Draw frames. Slubbers. | Intermediates. Rovers. Mule spin- 9 to 1.3 6 to 10 One frame of One frame of Two frames Four frames ning 18 to 24 80 to 100 of 120 to of 1G8 to 200 dels, divi- spindles 140 spdlea. spindles , ded into each each. three heads Bing frames Ditto Ditto Ditto Ditto Ditto Five frames of 168 to 200 1 spindles. The following are therefore the proportions of the above- named machines per slubbing spindle, respectively : — (deliveries) (spindle) (spindles) (spindles) 0-1125-0-15 0-075-0-1 0-075-0-01 VO 2-72-3-0 S-O-IO'O These proportions are those ruling in the bulk of spinning mills, and it is therefore reasonable to assume that they repre- sent what is found most useful. Drafts in Fly Frames. — The following are the factors control- ling the division of the combined attenuation required in the respective fly frame processes : — (1) Number of spindles of each type available ; (2) Speeds practicable ; (3) Extent of the combined attenuation required ; (4) Efficacious twist constant at each stage ; (5) Time lost at each stage. These decided, for example, as given below, the respective drafts are arrived at as follows : — Speed of spindles (per minute). Slubber, 550. Intermediate, 800. Rover, 1200. Per cent, time lost (approx.) Twist constant .... Proportions of spindles Count at each stage . . Draft at each stage . . . 1.5 1 1 c, 10 1 3 c. 7 1 8 Ca ^3 Total draft in these fly 1 frames j This is always fixed by the count of roving decided upon for spinning and by the weight of sliver, most suitable, at the drawing frame. AND COSTS OF YAKN 143 ]rHJi fixed quantities of fiy frames and S2)in)iin(j niacltincrij available, tJie adoption of the most suitable spindle speeds decide the drafts by fixing their capacity in respect of their twisting rates. The demands of the spinning machines having been ascertained, the highest rate at which the roving spindles can be satisfactorily run will decide the most suitable count of roving to prepare and also the draft in the spinning machine. Let the count of roving be denoted as x lbs. per spindle, and C3, C2, Ci, the counts of the roving, intermediate, and slubbing, respectively ; then the amounts required from the intermediates and slubber will be — 8c Intermediate, 3 per 8 roving, spindles, -^ o 8a; Slubber, 1 per 8 roving, spindles, — Hence the following equations : — Roving — 1200 X -^^ -— = ^^^ = X lbs. per minute per spindle VCg X C3 X 36 X 840 ^ ^ ^ Intermediate — 800 X tKir 8.^3 „ . . . ,, Slubber— 550 X — -- — — — LOO _ g,^ Y\)B. per minute per spindle x/Ci X Ci X 36 X 840 ^ ^ '- From the above equations the separate values of Ci, C2, and C3 may be found, when the sum of the draft involved in this production is known. The sum of the drafts in the rover, intermediate, and slubbing frames is found by ascertaining the weight per yard, or count, of the sliver at the finishing head of the draw frame that will produce the required weight when running at the most desirable speed, and comparing this with the count of roving required. An example is provided by assuming the conditions, in respect of the counts, deUvered, at the drawing and roving 144 COTTON SPJNNING CALCULATIONS frames : 0"2 and &0 respectively. Under these conditions the total draft or the attenuation in the slubber, intermediate, and roving frames would be = -^ x (2 X 2), the latter allow for the two doublings in each of the latter stages ; = 120. Therefore the weight produced per roving spindle per 55 hours 55 60 X 1200 X 93 ^ .^ „ = y -~-^ = 8'3 lbs. 36 ins. X 840 yds. x/6 6 100 (C3) (C3) The weight produced per intermediate | _ ^ q-q 11 = ^ X 8-3 lbs. spindle per 55 hours j 3 55 X 60 X 800 X 90 36^X 840 X -V/C2 X C2 X 100 3 .^ _ 55 X 60 X 800 X 90 X 3 _ - •'• ^'^^' - 36 X 840 X 100 X 8 X 8-3 ~ "^ .•. Co = 2-33, the count of the intermediate rove The weight produced per slubbing) _ 0.0 w 8 spindle per 55 hours j ~ 1 55 X 60 X 550 X 85 36 X 840 X -v/CT X Ci X 100 yyr n 55 X 60 X 550 X 85 _ „.,.^_ •' V ^1 X Oi - 3(3 X 840 X 8-3 X 8 x 100 " " ^^^ .-. Ci = 0*725, count of the slubbing sliver The drafts in the respective fly frames may be now ascer- tained from the above counts, and they are as follows : — Draft in the rover — count of roving X2 _6x2 ^.„ = 8-3x8 lbs. count of intermediate 2'33 Draft in the intermediate — count of inter, rove x 2 _ 2*33 x 2 count of slubbing ~ 0"725 = 6-43 AND COSTS OF YARN 145 Draft in the slubber — count of slnbbing _ 0*725 count of sliver 0'2 = 3-G25 It is seen, from this procedure, that the drafts in these machines depend not only upon the proportions of spindles, but also on the other productive factors mentioned on p. 142, and numbered 2, 3, 4, 5. Particulars of Fly Fbames, Machine. Eover . . . Intermediate Slubber . . Loss of time due to oiling, cleaning, and Usual sizes incidental of full stoppages bobbins, apart from dofiSng. Usual gauge?. Usual lift= Contents in ounces per bobbin. SP/o 4i" to 4J" 5f" Time lost per doff. ]i" to 3f " ! 5" to 51" 7" and 8" 8 to 11 oz.s. 12 mins. 6"to6J" 9" and 10"; 18to24ozs. 9" j 10" to 12" 24to30ozs. The Production in Fly Frames. — To estimate the production of the above-named machines. Eover, spindles making 1150 revolutions per minute ; hours worked, 55. Allow 5^ per cent, for loss occasioned through breakages, and proceed as follows : — Weight of contents] -.qq [the weight that would be delivered of full bobbin ii^f ^(n.^~l ^^ *^® period required to make a ) " "^ ^ ( doff, if no stoppages = {x) the weight in ounces _ I delivered by the roller in one minute, uninter- rupted vi^orking = (.?/) ounces 1150 X 16 twist per inch x 36 x 840 X count 55 X 60 = minutes required to fill a set of bobbins y ■X . ,. 1 . • 1 ft- r minutes taken to fill and - + time lost m doflmg = { ^^g- ^ ^^^ ^^ ^^^^-^^ ^ ^^^ /weight of contents oh _ ^production per spindle in ^ a bobbin in ounces / ~ t ounces per week 146 COTTON SPINNING CALCULATIONS Therefore, with the count produced by the roving 6, the twist constant 1*2, and the contents of a full bobbin 10 ozs., the production per spindle in ounces and hanks per 55 hours, respectively, would be — 55 X 60 100 10 X ^rT:v 1150 X 16 \/6 X 1-2 X 36 X 840 X 6 X 10 = 103-52 ozs. Hanks = l°«-:f^-« = 38-8125 lb With the count produced by the intermediate 2-33, the twist constant 1*2, and the contents of a full bobbin 22 ozs., the production per spindle in ounces and hanks per 55 hours respectively, would be — 55 X 60 ^ 100 / "" 94-5 + 12 X 22 = ^11^^22 = 294 ozs. 800 X 16 Zd5 + iZ ^2-33 X 1-2 X 36 X 840 x 2-33 ^ , 294 X 2-33 .o Q Hanks = ^- — = 42-8 lb With the count produced by the slubber 0"715, the twist constant 1*2, and the contents of a full bobbin 28 ozs., the production per week in ounces and hanks per 55 hours respectively, would be — 55 X 60 ^ 28 X^ ^^ ^ 94-5 + 12 r^ ^^ " ^^^^ ^^^• 550 X 16 V^O-725 X 1-2 X 36 X 840 X 0-725 J „ , 1055 X 0-725 ,„ Hanks = z.^ = 47 lb AND COSTS OF YARN 147 Examples of arranging the speeds, drafts, and counts to suit the mill specification. The following being the quantities of each kind of machinery, ascertain the suitable speeds, drafts, and counts. Spinning spindles, mule — . 32 pairs weft IJ" gauge, 64" + 4" draw IG twist If Total spindles Spindlea. 83,688 34,488 118,176 The weft are engaged upon, average counts, 46^ „ twist ,, ,, „ 36' The production of these per 55. j hours would be about 27i hanks of 46^ W. ; 29i hanks of 36' T. The other machines — Roving. Intermediate. Slubber. Dr. F.R. Cards. Scutchers. Number of frames Spindlea or beads Gauge .... Lift 60 176 8 in 20f' 7" 24 140 8 in 26" 10" 12 96 4 in 19" 10" 12 (3 beads 2 x 4| \of 8 dels, each/ 18 120 45" 8 4 laps up 45" Reasonable allowances in such a mill — ■ Doffing, mins. Cleaning. Stoppages. Other loss. Weight on bobbin. hrs. mins. per doff per cent. 07.S. Mule .... 8 '^ — ^ — liovers .... Intermediates . 12 12 •> U 22 Slubbers . . . 14 ft 14 " 28 Suitable roving for the above counts of yarn : 5^ for weft and 4i hank for the twist. The relative productive rates in the roving frames — Count 5^ X y/5^ = time per lb. 5^ „ 4^ X ^U = „ U 148 COTTON SPINNING CALCULATIONS If all 5^-liank rovings were produced, the total weight would be — 28160_Xv/:4L >^ =20,777 lbs. + 50,280 lbs. = 71,057 lbs. The amount of 4^-hank roving required per week is 28,160 lbs. The number of roving spindles required to prepare 50,280 lbs. of 5i-hank must be — 50280 10,560 total roving spindles x rfjonrj = 7472, say 42 frames Leaving 18 frames for the 4^ hank. Another way of arriving at the number of roving spindles to engage on each count is — 50,280 lbs. of 5i hank = 276,540 hanks 28,160 lbs. of 41 „ =126,720 „ 403,260 „ Therefore, if 60 frames of 176 spindles produce the above, and the respective productive ratios are — For 4^^ 4:}j X v^5i in hanks or length then the number of frames required for 126,720 hanks of 4J* — - 60 x^^^^™x^^- 18 frames -^^"^ 403260 ^ ^51 " and for 276,540 hanks of 5^^— = 60 X ?L6|40 ^ VSi ^ ,2 ,^^^^^ 403260 ^4^ The production of the fly frames, drawing frames, and cards, in pounds, must be as follows, allowing i per cent, for waste at each stage : — 5^ hank : Production, in pounds, per roving spindle — 50280 X 1 00 _ 42 X 176 X 99h~ v^^^^i^ AND COSTS OF YARN 149 U hank : Production, in pounds, per roving spindle— 21860 j<JOO_ ; 18 X 176 X 991 ~ 8-93 Production, in pounds, per intermediate spindle. All these frames making the same count— 78440 X 100 3360 X 99 ~ Production, in pounds, per slubbing spindle— 78440 X 100 _ ll52"x 98i~ ^^'^^ Production, in pounds, per draw frame delivery— 78440 X 100 ~96~>r98~ = S^4 lbs. Weight per card (see later). The Speeds of the Spindles in the Roving Frames.— Takin^r the twist constants at 1-2 in each of the fly frames, and" the stoppages and allowances as indicated, proceed to ascertain the rate of rotation of the spindles. Eoving, 51 hank : The doffs per week— The time to complete a set of bobbins and doff— 97- ^ (551 - 21)- ~ - 119-28 (mins. per doffing) 9^94 = 5 hours Speed of spindles ; revolutions per minute— . 11 X 51 X 840 X 36 X ^51 X 1-2 " 16 5~>r60 " = ^^^^ Koving, 41 hank : The doffs per week— 8-93 X 16 _ - J-J-- = 12-993 150 COTTON SPINNING CALCULATIONS The time to complete a set of bobbius and doff- Q7J- (55L - 2i)^ - 12-993 X 12 mins. ^^.^ ^^^ = T^^. = 3-78 hours 12-993 12-993 The Count of the Intermediate Roving. — The weight on an intermediate bobbin = 22 ozs. Eevolutions of spindle per minute, 800 ; allowances : 12 minutes each doff, and 2|- per cent, after 2i hours for cleaning. rr,. 1 , . -. rv> 23-6 Ibs. X 16 .^ ^^.. . Time lost m doffing = ^ X 12 = 206 mms. 97I- Nett time working = 53 hrs. - 206 mins. x ^r^ = 2887 mins. •'• ^^' ^^^^^* = 24-3 X 700 2887 X 800 l-2\/Cx 36 ) 25 X 2887 X 800 3 X 24-3 X 7000 X v/C X 12 x 36 2-63 The count = :. count X \/count = 2'63 .'. count = 1-90 The Count of the Slubbing Rove. — The weight of the slubbing bobbin = 28 ozs. Eevolutions of spindles, 600 ; allowances : 14 minutes per doff, and 2i per cent, after 2^ hours for cleaning. The production required per spindle per week = 69" 12 lbs. Time lost in doffing = ^^^ x 14 = 553 mins. 971 Nett time working = 53 hrs. - 553 mins. x —^ = 2547 mins. AND COSTS OF YARN 151 The count = gcj-ic/x 7 000 f '2547 X 600 I l-2v/Cx 36 ) 25 X 2547 X 600 The count 3 X 69-12 X 7000 X 1-2 X V'C X 36 0-663 Count X v/count = 0-737 The Count of the Sliver at the Drawing Frame.— Third head ; weight per dehvery, 834 lbs.; speed of F.Pw, 320; 1-^ inch diameter ; allowances : 2^ hours for cleaning and 2^ hours for breakages. Length delivery per week in yards = 320 X ^ X ^ X 60 X 53 X ^^^ Weight of the sliver delivery in grains per yard _ 834j^7_000^^^^6j<^2O00 ^ ^^ .^^^ ~ 320 X It X 22 X 60 X 53 X 97i Drafts. The Drafts up to this stage. Slubber = ^ ^^ ^^ = 4-33 Intermediate = ^ rron =5-16 u- tot Piover for 5h = -^^rrr- - 5 ^ 1-9 Rover for 4^ = -^. .^ = 4-73 1-9 152 COTTON SPINNING CALCULATIONS Weight of Card the Sliver. — Number of cards, 120 ; allow 4 for grinding. Hours worked, actual, 55, less 2h per cent. — 78440 ^ 100 ^^„ „ -j^ X -^Y = ^97 lbs., say 700 Revolutions of doffer 15 per minute 26 inches diameter. Weight of sliver per yard — 7000 X 700 . . „ ■ ofi — oo cvfi = ^^'7 grams Analysis of the Action of Deawing Rollers. Provided it is reasonable to assume that top rollers move at the rate of the cotton with which they are in contact, then Figs. 28 and 29 are records of the action of the drawing rollers in the various frames, under ordinary working conditions. Fig. 29 gives the particulars of the observed relative move- ment in slubber, intermediate, roving, and spinning machines. Draft: -^1045-^<-5-7 -^ Revs: 37 33 63 Cir; f71 mm] p4 mmA p2 mm., fv y tv yv y^ Dpaft;0-96>^-<1-15>— < >— CIO Revs: 10 8-5 41f Draft: .^ i -24 -^<-5-2-^ Fig. 28a. Cir: > (80 ni m V |70 m m) (80 m m . Revs: 31|- 40^ ^if-^ Draft: _j_i.255-^-^502-^ Fig. 28b. Those, subsequently given, marked S.W. being of the self- weighted type, i.e. only the front top roller being weighte.i. The rest are of the ordinary weighted type. Figs. 28a, 28b, show the manner of obtaining the data. The revolutions given are exclusively in respect of each pair of rollers (bottom and top). The relative rotation of the different lines are contained in the draft. In these figures the rollers are arranged in the order of their AND COSTS OF YARN 153 sequence, from left to rigbt, back to front. Their circumference, revolutions, and draft are placed opposite the parts to which they refer. The top line of numerals, in figs., are the observed ratio in the movement, or draft, in the top rollers, in each instance in terms of one of the precedent roller. Thus, 1'003 is that of the second in terms of 1 unit of movement of the first top roller. The middle line of numerals relate to the difference in the movement of the top and the bottom rollers in terms of one of the latter. The bottom line of numerals gives the ratio between the bottom SLUBBER INTERMEDIATE ROVER ^1-15 -^4-32-^ ^1.045^5-7-^ ^V013^3.98-^ 1-015 107 0-982 0-962 Vie 1008 1-0 1-205 1-0 Vl-218-J<~3-97j V-T 255^:^5 02 -J' V-1-21 5 J«_3-31-5y ROVER (S.W.) RING FRAMECS.W.) 1'003-^P$— 6-4 -^ fg- 108 - > T < -7-05->» ^V003-^6-4-^ ^1-08-^ 1-(l 1-287 1-005 1-Q2 1-125 10 lU-l 24 -i- 5 2 -i >L 1 21 JU^6 36 -J Fig. 29. lines of rollers, in each instance, in terms of one of the precedent roller. The features most noticeable, fig. 29, are the variations in the slip of the cotton, indicated by the movement of the respective top rollers. Except in the slubbing frame, this slip is consider- able. With that exception the effect of the action of the first and second pairs of rollers appears to be only that attributable to the elasticity of the rove, being : 4"5 per cent, in the intermediate, 1'3 per cent, in one rover and 03 per cent, in the other rover, whilst it is almost 8 per cent, in the ring frame. The Functioiis of the Respective Lines of Draw Rollers. — There are no reasons for suspecting that the ratios given in the last paragraph differ from those generally obtaining. Those results imply that the functions of the middle and back top rollers are, first, that of obtaining a uniform tension in that portion 154 COTTON SPINNING CALCULATIONS of the rove between them ; second, that of controlhng the body of fibres not within the nip of the front pair of rollers. If these inferences are true, it cannot be an advantage to place the middle and back rollers widely apart, also in having a draft greater than that which covers the possible variations in tension and natural elasticity of the rove. For these reasons the draft between the first and second lines of rollers should always be low and in accordance with the last-named conditions. The difference in the condition in which the cotton is presented in the slubber, accounts for the almost complete realization of the draft between the first and second lines of rollers in that machine. Front rollep Hank Indicators. Figs. 30 and 31 contain the gear common in the old and new types of hank indicators used in drawing, fly, and ring frames. In Fig. 30 the dial is numbered from to 100, and this part is connected with the front roller by the following train of wheels : A single worm on the front roller drives a worm wheel of 51 teeth, the subsequent gear being „ . ^ - drivers ,, .6_ _5 _5 . •!_ thp 6o» 60» 60» 60' (Jriven' latter denominator being the dial wheel. This form of indicator does not admit of reliable fractional readings, and for this reason is being discarded. The above gear is only applicable to frames containing a front roller 1^ inch in diameter. An allowance of 2| per cent, is always made for breakages, so that the indicator registers 2^ per cent, less than the actual length delivered. Fig. 30. AND COSTS OF YARN 155 111 the present instance the actual length delivered per 100 hanks registered would be — GO X GO X 60 X GO x 51 x Ij, x 22 X 1 5X5 x5xGxlx36x7x840 = 103-04 This is equal to an allowance of 2"95 per cent. The particulars of the size of roller and of the gear are now stamped upon each indicator. ExiCRCiSE 1. — Assuming the other gear as above, what size of worm wheel would be suitable for 1 J, If, and 1^ inch in diameters of rollers ? Ans. 46, 41, 38. Exercise 2. — What lengths, in hanks, would be delivered per 100 indicated, if the indicators used in frames, containing front rollers f, 1, 1}, If, and 1.^ inch in diameter, were geared as in Fig. 30, with the exception of the worm wheels, these latter being 65, 57, 46, 41, 38, respectivety ? Ans. 102, 102-5, 103, 100-9, 102-3. ExERCisK 3. — What weight would be produced in 10 hours per frame of 186 spindles if 9-4 hanks are recorded and the count of the rove is 3-5 ? Ans. 500 lbs. Exercise 4. — At what rate would it be necessary to run the spindles per minute, if the loss of time, including doffing, was 5 per cent., tlie twist per inch 2-2, and the count 3i, in order to register on the indicator 9-4 hanks in 10 hours? " ^«s. 1125. In Fig. 31 there are three index discs, that on the left hand recording tens, that in the centre the units, and that on the right hand the decimals, each disc being numbered from 1 to 10 and each free upon the central spindle. The driving from the front roller is by a worm driving the 36, and thence to the decimal dial wheel : the gear is •2 4 _^8 2 0' The units dial is driven from the decimal dial by a train ^ X .f^y, and the tens dial is driven from the latter by Fig 2 0" Thus the calculated length delivered per 100 recorded- 20x4x20x4 X 20x4x24 X36x9x22x 1 X 1 ~ 8x1x8x1x8x1x1 Xl X8X7X36X840 = 101 hanks 156 COTTON SPINNING CALCULATIONS Exercise 5. — What length iu hanks would be delivered per 100 recorded if the 36 worm wheel is changed to 37 ? Ans. 103-8. Exercise 6. — What length in hanks would be delivered per 100 recorded if the 36 and 34 worm wheels are changed to 35 and 25? Ans. 102*3. Exercise 7. — What w^eight of 4' roving will be produced in a frame containing 200 spindles per 52 hanks recorded by an indicator, as in Fig. 31, assuming the loss is actually 2i per cent. ? Ans. 2560 lbs. Length or Full Bobbin Stop Motions. Fig. 32 represents a length stop motion applicable in fine work when a number of sets of bobbins are required containing exactly the same length. This motion is very ^"i^^ c 1 °^^° convenient in the preparation of special rove I-— H- ni for spinning samples and small quantities, and O P"i I n "when not more than the roving necessary to make the yarn is required. A is a worm on the front roller, B a worm Fig. 32. wheel, C a worm on the latter, driving D, D is compounded with the worm E ; E drives F, and this is attached to a peg disc G ; a suspended catch H operates the strap control release bar I at each revolution of G. B is the change wheel. The length of roving delivered per action of this motion with the front roller 1' inch in diameter = ^ X ^^ X ^- X ^^4^ 1 1 1 do = 4295 yards. Exercise 1. — What size of change wheel (35) would be required to make bobbins containing 21 leas, 73 yards? Ans. 27. Exercise 2. — A roving frame containing 200 spindles is required to prepare 500 lbs. of 20' roving for a mule using double roving and containing 1000 spindles. What change wheel will give the nearest approach to the necessary length on each bobbin ? Ans. 34. Exercise 3. — What lengths of roving will be delivered by the front roller per action of this part with change wheels ranging from 25 to 45 respectively ? Mule Calculations. The Gearing in Mules. — The parts engaged during spinning receive their motion from the rim shaft.- Those parts that are engaged whilst spinning is in abeyance AND COSTS OF YARN 157 receive their motion through the shaft designated the backing- oflf and taking-up motions shaft. The rim and the backing-off and taking-up motions shaft receive their movement from the line shaft, usually through the medium of a counter shaft. This system of driving obtains better control than when driven direct from the line shaft. The draft gear in these machines is identical with that in the fly, and ring frames. Eeference to those will make clear all that can be said respecting drafts and changes in the counts in mules. Examples are given later in this section. (a) The spindles are connected with the rim shaft by an indirect train, comprising two direct trains of pulleys and bands, the rope from the pulley on the rim shaft being guided to one on the tin roller shaft by suitable carriers. The last-named shaft is coupled to a series of long drums known as tin rollers, these drive bands conveying the motion to grooved pulleys or wharves on the spindles. The rim pulley is the usual change part in this train. In some makes slight changes are also arranged for, in the size of the tin roller pulley ; it is then made in two detachable portions. When a change in the speed of the spindle is expedient, this change is used for altering the rate of rotation of the spindle and its relation with other parts. (b) The connecting gear from the rim shaft to the front roller, in most makes of mules, consists of an indirect train of six wheels, arranged in three direct or simple trains. These are conveniently mounted to enable at least one driver and one driven wheel to be changed. A change in the value of this train is necessary when an alteration in the relation of the rollers with the rim shaft is required. Also, when a change in the speed of the spindle is desired, but without any alteration in the relation between this part and the rollers. (e) The front roller is connected with the back roller by an indirect train of four wheels comprising two direct trains. These wheels are named the draft wheels and, respectively, the front roller, crown, pinion, and back roller wheels. The two latter are conveniently mounted for changing, being the medium of alterations in the draft. The middle back rollers are connected by a direct train. 158 COTTON SPINXIXG CALCULATIONS comprising three wheels, in the same manner as in fly frames. ((/) The carriage, of spindles, is drawn outward by two sets of ropes attached to drums secured upon the back shaft. The latter being connected with the front rollers by an indirect train of five wheels, these comprise two direct trains. Those wheels are conveniently arranged to enable a driven and a driver to be changed. They are known as the gain and gain boss wheels respectively, the last named driving the wheel on the back shaft. These wheels are the medium of alterations in the rate of movement of the carriage, relative to that of the front roller ; and therefore they control the tension in the yarn during spinning. In spinning the poorer classes of yarn gain is often a minus quantity. The "jacking," " ratching," or stretching motion is the means by which yarns may be improved, during spinning, by the elimination of soft thick portions. The motion is not usually adopted for other than fine work, because it reduces the production considerably, thereby increasing the cost of spinning. It is the medium for actuating the backshaft train at } to I the normal rate, and during this action the rollers are either at rest or moving at an almost imperceptible rate. This action has the effect of moving the carriage at from ^ to I of the normal speed, and hence the yarn is stretched and made more uniform by the thicker portions being attenuated. In accom- plishing this successfully it is necessary that the 3'arn should only receive a portion of its twist prior to this action. The exact amount cannot be stated, because it varies in extent, with the circumstances, from -^ to | of that required, being lowest in the best-prepared and long-stapled cottons. When the com- pleted yarn contains above the standard twist, much twisting is necessary "at the head." This, if completed at the ordinary speed of the spindle, results in a considerable loss of time. The gearing, comprised in this motion, varies in the different makes. Three types are contained in Figs. 34, 36, 37, and 38. (e) The slow roller turning, or " receding," motion, contained in Figs. 34 and 36, consists of a train of wheels in uninterrupted connection with the rim shaft. This prevents the front roller from being at rest whilst the rim shaft is rotating in the AND COSTS OF YARN 159 "twisting" direction. Tiiis action eliminates the tendency of ** twisting down " of the ends during jacking. It is constructed with an escapement allowing the front roller to be driven by the major movement active. The twisting motion, shown in Figs. 34 and 36, controls the twist. It is only used in those mules wherein the twist cannot be, advantageously, completely inserted whilst the carriage is moving, necessitating the completion of twisting with the carriage at rest at the "head." This motion controls the rim shaft driving strap. The mechanism consists of a detent catch for holding the strap fork lever, this is released by a " tumbler" operated by a train of wheels that are in connection with the rim shaft. One or two of these wheels are mounted conveniently for changing. These change wheels are termed the twist wheels because they control the revolutions which the rim and the tin roller shaft and the spindles make per draw, and thus the twist inserted in the yarn. The double speed motion, for rotating the spindles at two different rates, aims at the reduction of the time occupied in spinning, when "jacking " is in vogue, by actuating the spindles at the maximum rate throughout. Prior to jacking, the speed of the spindles must be in accordance with the resistance of the yarn. As the degree of twist increases and improves the strength of the yarn, the spindles are rotated at a higher speed, some- times almost double the former rate. For this work two drums of different sizes may be employed, to drive the counter shaft alternately, as shown in Fig. 35. Two different sizes of rims separately driven are also used for the same purpose. The building motion consists of a mechanism for raising the range of movement of the directing faller wire so that the yarn is laid in layers, progressively ascending, upon the spindle. The rate of this movement determines the thickness of the body of yarn so formed, and therefore that of the cop. The parts actuating this movement are : a screw, which operates the with- drawal of the inclined plates supporting the copping rail, having a ratchet wheel secured to it — the latter being actuated, by the passage of a curved or inclined bracket secured to the 160 COTTON SPINNING CALCULATIONS carriage front ; an adjustable number of teeth per draw, through the medium of a pawl and pawl lever. The pawl lever, at each passage, is pushed prior to the termination of each outward movement of the carriage. The extent of this movement is adjusted by varying the inclination of the curved bracket, and also, by the use of screws of difterent pitch. Eatchet wheels are made a standard diameter by each maker, but with varying numbers of teeth. Whenever convenient the wheel is moved one tooth per draw only. The Roller Delivery Motion, during Winding. — This motion usually consists of a direct train, composed of three wheels, for driving the front rollers during the inward run of the carriage. This is effected from the back shaft. The wheel on the latter, or that on the front roller, is furnished with an escapement that allows of the front roller being driven by the major movement active. The winding motion is similar in construction in all the types of mules in general use. It consists of an actuating chain and chain barrel, with a direct train connection to a wheel on the tin roller shaft. This generally consists of two wheels, one of these communicating the movement to the shaft through an escaj^ement that allows the tin roller to be always under the influence of the major movement. The rate at which the chain is unwound from the barrel controls the spindle. The rate of the unwinding of the chain is determined by the radius described by the other end of the chain. This is secured to a nut on a screw within the quadrant arm, the screw being actuated in one direction only, and this increases the radius described by the nut. This is the function of the automatic winder governing motion. The backing-off and taking-in motion is shown in each of the Figs. 33 and 34. This is the same in all types of mules except that the value of the train and rate of movement are varied. During recent years considerable improvement has been made in this motion. The change enables the tension, to which the yarn is subjected, to be adjusted in the most desirable degree. This is obtained by the introduction of parts which control the engagement of the backing-off friction, and allow this to be deferred until the momentum of the rim shaft is reduced to AND COSTS OF YAKN 161 the desired degree. The effects are that backing-off frictions may be run at slower rates and are more reliable. They can be adjusted more definitely to the requirements. The Hastening Motion. — The usefulness of self-acting mules for the finest counts has been improved by the introduction of figure 35 type of this motion. Its aims are to secure the desired adjustment in the number and spacing of the coils wound upon the spindle at the termination of winding. Also, to relieve thereby the strain upon the yarn during the action of bacldng-off. Twist. — The following are the common twist constants' standards in connection with the ordinary qualities of single yarns : — Descriptiou of the V count x constant cotton and yarn. = twist per inch. Egyptian weft 3-18 American „ 3'25 Doubling „ 3-49 American twist 3*75 Egyptian „ 3-606 Ring „ 4-0 The Conditions governing the Various Changes in the Wheel Train Values in Mules. — (1) The speed of the spindle should be the highest consistent with the quality of yarn required, and with due regard to the wear and tear of the machine. The rim pulley is the medium of alteration. (2) The twist required in the yarn must conform with the standards given above. This controls the sizes of the rims, twist and speed wheels. « (3) The most beneficial rate at which the carriage may be moved outward often restricts the speed at which the spindles run, and determines the size of the speed wheel. Five draws in 60 seconds is considered the maximum rate at which the carriage may be worked. (4) The count of the roving available and that of the yarn desired. (5) The "gain" or ''drag" must be governed by circum- stances ; generally it is beneficial in attenuating the thick soft and breaking the weak parts of the yarn. At the same time it M 162 COTTON SPINNING CALCULATIONS eliminates snarls, and is usually applied to the greatest extent practicable. This governs the relation between the movement of the carriage and rollers. (6) "Jacking" or "ratch" can only be adopted when time and other circumstances permit. Generally it is only adopted to a very limited extent in other sections than the production of fine yarns. It is essential in the production of yarns of a superior quality ; sometimes it is applied to the extent of as much as 4^ inches in a draw of 60 inches. (7) The " shaper" wheel governs the thickness of the cop. In changing, the following precautions should be noted : — (1) Avoid changing the twist by means of either the speed wheel or rim pulley before ascertaining whether a change in the spindle or carriage speed will be most beneficial, and to what extent each of these may be altered to advantage. (2) Before changing the twist wheel, consider whether the proposed alteration can be accomplished to greater advantage by means of the rim or speed wheel. (3) Always notice and collect data of the difference between the calculated and actual results. These vary very considerably in the non-positive gear, and can only be satisfactorily deter- mined in this way. (4) Check the accuracy of the effects of the draft. This is readily done at the spindle point by taking a sufficient number of ends, of a standard length, to enable the counts to be ascertained. (5) The differences in the rate of spindles vary very much, and in ascertaining the actual twist, several tests should be made. Calculations and other Particulars of the Various Trains of Gearing. Fig. 33 is a plan of the gearing as found in the Hetherington mule for coarse and medium counts- The particulars relating to the driving of the rim shaft in this figure are — Line shaft, 235 revolutions per minute ; diameter of drum, 32 inches. Counter shaft : fast and loose pulleys, 16 inches ; driving drum, 28 inches diameters. AND COSTS OF YARN 163 Revolutions of tlic rim shaft jX'V minute — 235 X 32 X 28 16 X 14 = 940 (a) Revolutions of the spindles per minute, when the rim pulley is 12 inches and the tin roller pulley 12 inches — 940 X 12 X 6 12 X 5 = 7520 50 Taking in ^?7 ^sha ft 2f revs. per draw 75 Back Shaft 3rrevs.= 64' 10/ Fig. 33. Therefore, the different speeds of the spindles obtainable by the range in the sizes of rims (12 to 22 inches) are = 13" 14" 15" 16" 17" Size of rim 12" SizeofT.KP 12" Revs, of spindle per miu. 7520 8150 8780 9420 10,050 10,080 164 COTTON SPINNING CALCULATIONS Size of rim 18" 19" 20" 21" 22" Size of T.E.P 12" Kevs. of spindle per min. 11,300 11,730 12,530 12,970 13,600 2sfoTE. The actual will differ considerably from the calculated speed. The loss between the rim shaft and the spindle will be from 5 per cent, upwards, when the diameters of the surfaces in the train are measured in the customary way. (h) The rate of rotation of the front roller relative to the spindles is varied in order to obtain the desired twist. The train connecting the front roller with the rim shaft is provided with suitable change gear for that purpose. The length delivered by the front roller during the outward run of the carriage, varies with the amount that the latter is desired to *'gain." The movement by the carriage is from 68 inches to 58| inches, the former in mules for coarse, and the latter in those for fine, work. Assuming no " gain," the surface rates of the movement of the rollers and carriage correspond. Thus, with the front roller 1 inch in diameter and the draw 64 inches, the front roller makes — -jj — 22" = 2^A revolutions per draw With the gearing from the rim shaft to the rollers arranged to give the quickest movement practicable within the range of change wheels stated : the largest driver and the smallest driven change wheels must be adopted ; whilst in the train from the rim shaft to the spindles, the smallest drivers and the largest driven change wheels are necessary. Thus, neglecting the slippage arising in respect of the connection to the spindles, the revolutions of the spindle per 20 1\ revolutions of the front roller would be — 20 4 X 38 X 35 X 40 X 12 X 6 ^ "^^11 ^ 20 X 35 X 30 X 12 X I This represents the least twist per draw under the conditions named, 412*5 The twist per inch of yarn is therefore ^^^ = 6*44. Thus, driver wheels and driven pulleys in this connection 29 28 27 26 25 24 426 441 457 475 494 515 6-66 0-88 7-14 7-43 7-82 8-05 22 21 20 19 18 17 562 588 618 650 687 728 AND COSTS OF YARN 165 reduce the twist inversely to changes in their size, whilst driven wheels and driver pullej's have the inverse effect. Therefore, the revolutions of the spindles per draw and the twist inserted per inch of yarn spun, with other change wheels than those given in the previous calculations, are as follows : — (pi) Size of wheel on the rim shaft . 30 Eevs. of spindle per draw . . 412 Twist per inch 6-44 Size of wheel on the rim shaft . 23 Revs, of spindle per draw . . 537 Twist per inch 8-4 8-78 9-2 9-66 10-15 10-7 11-37 The revolutions of the spindles per draw possible with the range in speed-wheels (40-60), as specified, and the rest of the speed gear, excepting that a wheel of 17 teeth replaces the 30 on the rim shaft, as given in the previous calculation, are as follows : — The train from the rollers to the rim shaft when Of. y. Q" Tw obtains 728 revolutions of the spindle per draw of 20/^- revolutions of the front roller. The 40 in this train is the speed wheel and therefore increasing the size of this will cause a reduced rate of movement, by the rollers and carriage, inversely to the change in these wheels, and hence proportionately more twist in the following amounts : — (6,) Size of speed wheel . . 40 41 42 43 ... 50 ... 55 ... 60 Revs, of spindle per draw 728 746 764 782 .. . 910 .. . 1002 . . . 1092 Twist per inch .... 11-37 11-6 11-9 12-2 . . . 14-2 . . . 15-6 ... 17 FurLher increases in the twist may be obtained by increasing the value of this train. This may be accomplished by reducing the number of the teeth contained in the wheel on the same axis as the speed wheel (35), and also the bevel wheel (20), driving that on the front roller shaft. The latter is named the front roller clutch bevel. By replacing these with 27 and 17 respectively, the range of twist obtainable when a 60-speed wheel is also employed, becomes — 4 38 X 35 X 60 X 12 X 6 ^ ( 1670 revolutions of twist per ^^ 1 17 X 27 X 17 X 12 X ^ ( draw 45 . . . 50 . , , . 55 . . , . 60 1250 . . . . 1390 . . , . 1530 . . . 1670 195 . . . 21-6 . . . 23-8 . . . 26-1 166 COTTON SPINNING CALCULATIONS Thus : when the speed wheel is altered to 40 the twist per draw becomes — „„ 4 ^ 38 X 35 X 40 X 12 X 6 ...^ ^' 17 X 27 X 17 X 12 X ^ Hence, the revolutions of the spindles per draw and the twist per inch obtainable by using the various sizes of speed wheels comprised in the range will be — (Jg) Size of speed wheel . . 40 Revs, of spindle per draw 1112 Twist per inch .... 17-3 Assuming that, after the above-stated changes, the range in the sizes of the speed change wheels exhausted, further altera- tion in the twist would only be practicable by changes in the train of rope and band driving gear, from the rim shaft to the spindles. Such would, at the same time, alter the speed of the spindles as per paragraph (a). The changes in twist obtainable with the range in sizes of rim pulleys available, as specified, are — Size of rim in inches Twist per inch with the \ 40 appended speed wheels ) 60 Size of rim in inches Twist per inch with the? 40 = 24-5 appended speed wheels i 60 Basis 64 inches = draw. It is customary, also, to make the tin roller pulley in halves in order to admit of its being changed : the range is from 10 inches to 12 inches. In the present instance the latter is in use. Altering this would affect the twist and at the same time the speed of the spindles in the inverse proportion. (c) " Gain" Changes. — The back shaft, in pulling out the car- riage, is assumed to make a fixed movement. This is not exactly the case, because this movement must be subject to variations arising through differences in the tension of the ropes and matters influencing the resistance to the movement of the carriage. For the purpose of calculation it is convenient to 12 13 14 15 16 17-3 18-7 20-2 21-6 23-0 26-1 28-3 30-5 32-6 34-8 17 18 19 20 24-5 25-9 27-4 28-8 37 39-2 4L-4 43-5 AND COSTS OF YAKN 167 make the assumption named. In the present instance, the movement of the back shaft is taken at 3g revolutions per draw, so that with the smallest gain boss (25-27) and gain wheels (97-112), and with the rest of the connecting gear from the front roller to the back shaft as specified, the length delivered by the front roller during this movement would be — S^ X '^--^- = I "'•''' '^^ ^revolutions of the ^ 25 X 60 front roller per draw and therefore 17'46 x 1 x ^- = 54-87 inches delivered With the following **gain" change wheels, the length delivered by the front roller and the *' gain " would be : — Gain wheel 97 98 99 100 101 102 Gain boss wheel 25 25 25 25 25 25 Inches delivered by rollers per draw 5i-87 55-5 56-0 56-6 57-2 57-7 Gain in inches 9-13 8-5 8-0 7*4 6-8 6-3 Gain wheel 103 104 105 106 107 108 109 Gain boss wheel 25 25 25 25 25 25 25 Inches delivered by rollers per draw 58-3 58-8 59-4 60-0 60-G GM 61-7 Gain in inches 57 5-2 4*6 4-0 3-4 2-9 2-3 Gain wheel 110 111 112 112 111 110 Gain boss wheel 25 25 25 26 26 26 Inches delivered by rollers per draw 62-3 62-8 63-4 60-9 60-3 59-8 Gain in inches 1-7 1-2 0-6 3*1 37 4-2 Gain wheel 109 ... 112 111 110 109 .. . Gain boss wheel 26 ... 27 27 27 27 . . . Inches deHvered by rollers per draw 593 . . . 587 58-2 577 57-1 . . . Gain in inches 47 ... 5-3 5-8 6-3 6-9 ... The changes in the length delivered by the front roller per draw during the outward run of the carriage, is directly pro- portionate to the changes in the size of gain, and inversely in respect of the gain boss, wheels. Yarns highly twisted and of poor quality do not admit of the carriage gaining on the rollers. In such, the rollers more fre- quently deliver at a rate in excess of that moved by the carriage. This is sometimes as much as 10 per cent. In the production of the best qualities of yarn, when fully twisted as the carriage moves out, only a slight " gain " is practicable. *' Gain " is 168 COTTOK SPINNING CALCULATIONS most applicable with low spindle speeds and when the yarns are not fully twisted during the movement of the carriage. Changes in the Builder Wheel. — The approximate size of suit- able builder wheel, may be ascertained as follows, when the size of cop required is known : — -J- = suitable builder wheel dc b = the length in inches of the yarn contained in the cop. d = tJie length wound in inches per draw. c = the revolutions of the copping screw necessary in completing the cop. h, is ascertained from the weight of the cop in grains, divided by the weight of one hank in grains, and multiplied by the inches per hank. Thus — nettTveishtrf^cop in grains ^ g^^ ^ gg ^^ count c, is ascertained by marking upon the spindle the length which the cop measures, from the cop bottom to the bottom of the chase; and then proceeding to turn the copping screw sufficient to pass the winding faller wire through the movement marked on the spindle, opposite. This must be done whilst the carriage is at rest, with the trail lever bowl on the ridge of the copping rail, and the revolutions of the screw counted. Ascertaining the Suitable Builder Wheel in changing Counts. — Changing the counts affect the weight of the cops in the inverse proportions, and, assuming the tension of the yarn during winding proportional to the area of the yarn, the diameter of the cop would be affected in the inverse proportion to the ^/counts. Thus, the mode of calculating this wheel, in order to obtain a cop of constant size, should be as follows : — Present wheel X ^required count ^ ^^^^.^,^^ ^^^^^ ^/present count Note. — A difference in the size of the cop must alwaj's result when the yarn is wound at other tension than inversely proportional to the difference in the area AND COSTS OF YARN 169 of the yarn. Also, when (lie change alters the quality of the yarn in any way, the difficulty of adjusting the tension in the correct order is such that the above rule cannot be relied upon. The following rule will be found more reliable but must not be regarded as accurate in all cases : — ' Required wheel = Pi'esent wh^Vrequire d^ount _^ present wheel x required count 2v'present count 2 x present count Ascertaining the suitable builder wheel in changing the size of the cops only — ^ ' Present wheel (diameter of requi red cop)2 (diameter of present cop)^ The following are exercises in calculating the alterations necessary to adapt the gearing in Fig. 33 for the work given. They are given in tabulated form because it is more convenient Allow 10 per cent, for slippage in the driving of the spindles from the rim shaft, and use the customary twist constants where the twist is not given. Explanation of the tahulated exerdscs.—llho^Q columns numbered 1 to 16 are separate exercises. The data required is signified by (?). Base the calculations for the builder wheel on that given in Exercise 1. The items referred to in each column are contained opposite in the first two columns on the left hand. 170 COTTON SPINNING CALCULATIONS ■73 - - - - CV. - 10 oc lO 00 w CV, c^ - c»- CV, -- I- 00 T-( ^ h 13 +, C5 =^^^ !>'-' (M '*' c- CO 1-H :o cw c>- - .. 0- CD Cv. cw Ci 0<l Cv. <:^- c. c^. CV, CO Cv, 0^ 1— 1 1-H oOJ CV, CV-. c^ 0- Cv, CV. in Oi o (S^' in +. He c^ Cv. CW CV, 05 10 0" r-l H^" 02 +. Oi -oco •-«" ^ c>- c^ CV, Cv, CO CV, c:5 0" H< OS +. c 00 ■* CV- cv, CV, CV. CO CV, C5 10 0" ^"^' 00 +. t> HUM CO cv, CV. cv. c^. CO CV. c: •0 0" H<i +. 05 o CO cv. CV. cv. CV, CV, CO ^< m +. o CV^ CV. C5 00 H^' ao +, Tf< CV, 0- CV, 's^ -t< 05 M 00 [>« c^ CV, CV, CV, %tl '* CO - Ci H<: ai » cq O02 (M 0-. cv< CV. CV^ " CO CO T— 1 cop C^ 0- CV. CV. - CO c^. CV. CO 3 3 . H H S'fe a s 1 1 s a rH CO a en S S 3 03 11 § >• 1- © Cm 3 >^ _; — , ^ '53 ■" (3 2 ® ^'6 II g '53 II 00 5 !3 ci 2 'a c3 '0 ® — en "^ • - (D » a Si CO '2 •5 a^ a 13 — 'C °^ iU ^ ^ £ 3 QTJ 2 i1 a 3 'o > 00 c3 'a, o< 30 ^ "5 33 '■2 "3 (1 ^t3 2 0) "^ CI W Q Q cc OQ « H <«J ^ w AND COSTS OF YARN 171 ^ ^ ;=; ^ s '^ (M (M o c m — , ^•1 l^ ; O S-l e? CD CO (M ?-H (M ri O i-t O 5^ l^ 1 (>4 ^1 ->) '"' '~' Ch 03 rj tH " "^ rr, r-- 5 "^ 03 _^ ^ a E -2 _ !0 t- ^ t^ a ^fl 0) S.S.- a-C^S " - "^ 2 5^-2 cc en '^ 03 ^ 03 i: _ <c a « -M P .- T' a. o ^ o ^ a 2 ■2 '5 ft « 172 COTTON SPINNING CALCULATIONS Examples in Calculatixg the Exercises on Page 170-1. The following changes would be necessary to adapt the gear in Fig. 33 for the conditions stated : — ExEKCiSE 1. — To drive the spindles at 6000 revolutions per minute, actual, with a 12-inch rim: The calculated rate of the spindles will = ^^^^on ^^^ = ^^^^ ^^^ •'' *^^^ Revolutions of Rim Shaft. — With the minimum and maximum sizes of driver and driven change pulleys respectively (see par. (a), p. 163) — Revolutions of the rim shaft per minute = ^^^^ ^ i^]l = 834 6 X 12 Speed and Twist Changes. — The front roller, if 1 inch in diameter, and there is 64" X 7 no gam, will be required to make — ^ — = 20i\ revolutions per draw. During this movement the spindles are required to insert twist to the extent of 3-75 v'S = 10-6 per inch, or 3-75^8 x 64 (inches per draw) = 753, actual; and therefore the calculated revolutions of the spindle per draw are ^^ = 837, or -S^j^ = 13-1 calculated twist per inch. The train of gear connecting the spindle and the front roller (see pars, (a), (b), pp. 163-4) must therefore have the following value : |^ = ^^\^/^ = 41-1. According to the range in the change wheels given in Fig. 33 the lowest , .,,.,.. 6-0 x 12 X 40 X 35 X 38 ^^ „ value of this tram is ,r-^r^ ^- ^-r — -~ -— = 20-2. 0-75 X 12 X 30 X 35 X 20 Hence, altering the value of any of the wheels contained in this train, to increase their ratio 20*2 to 41-1, will have the effect desired. Namely, changing the twist to 13*1 calculated. (driven) 40 . 40 41-1 Therefore the wheels 7.^ = 1-3 must be altered in value to oq x oKTo (driver) - "= ' - 20 Therefore the required wheel on rim shaft = 20, and the speed wheel = 54. For "Gain" Wheel, see pp. 166-7. The Draft required in the rollers is that necessary to attenuate 11' to 8 16 8' count, or y^ = -o- = 5|. By assuming the draft change pinion necessary, Ig o X, the following equation is obtained : — 54 130 1 Ki 54 130 ^ X 16 X I = ^ ••• ^ = 51 >< T6 The range of sizes of draft pinion wheels that can be accommodated is, approximately, from 30 to 60, and on the back roller from 40 to 60. The wheel AND COSTS OF YARN 173 82 is, therefore, too large, and hence it is necessarj' to reduce the size to within driver 82 the ransre of accommodation. The ratio of these two wheels is -r— = i^-, ° driven 54 or 1-52. Hence, any of the following pairs of wheels would be suitable for the 47 56 59 position: 31, 3--. 3C,- Exercise 6. — In this instance the length of yarn to be wound each draw is 64 + 4 inches, and hence the twist inserted must be in accordance therewith. Twist per inch required in the yarn wound = ^^24 x 3-75 = 18-4 /. Twist per draw = 68 inches x 18'4 = 1250 According to par. (^3), p. 163, the gear should be — tracing the train from the rim shaft to the F.R. : 17 driving 45, 27 driving 35, 17 driving 38 = 1250 revolutions of rim per draw; and therefore ^p = 18*4 twist per inch, this being with a 12-inch rim pulley and at the rate of 7520 revolutions of the spindle per minute. The Size of Eim. — The rate of the spindle required is 9500 revolutions per minute, actual; hence, with the rim shaft making 940 revolutions per minute, and the size of the rim x, and 10 per cent, allowed for slippage, the following equation is obtained : — 940 X a; X 6 9500 x 100 .^... = 10555 12 X I ~ 90 10555 X 12 X I i^o, .„ . , .'. X = pT-fT. 75 — ~ = 16*85, say 17 inches 940 X 6 ' -^ The revolutions of the spindles per draw, actual = 1250 Allowing for slippage, the calculated revolutions of spindle per draw = 1390 Proof that the above is satisfactory : — The Speed Train of Wheels. — The train connecting the rollers with the spindles 1390 must therefore have a value of ^tt-^ = 68-3. This means that the spindle must be calculated to move 68*3 revolutions per 1 of the F.E., and hence the following equation, when the speed wheel has the value x : — 68-3 X f X 12 X 17 X 27 X 17 _ . _ „. 6 X 17 X a; X 35 X 38 ~ . . x - 60 i Alternative sizes of suitable wheels : — The smallest speed wheel practicable being 40 (40-60), and the ratio required 17 between this and the wheel on the speed shaft being ^^, the follo'W'ing other wheels, within the range of accommodation, will give, approximately, the desired , 23 24 25 26 wheel on rim shaft results: ^g, ^, -^, g-^, gpeed wheel " The draft required in the rollers is that necessary to attenuate 3' roving 174 COTTON SPINNING CALCULATIONS into 24' = --g^ = 8. B}- assuming x tlie draft claange pinion, the following equation is obtained : — 54 X 130 X 1 Q . 54 X 130 ^. -^. ., _. , ^ -^ . =8 :.x- ^ -^ = 55, Draft pinion a;xl6xl 8x16 12 X a/24 12 X 24 Builder Avlieel = ^ y + . t = 10-4 + 18 = say 28 2 »/ 8 / X o Exercise 7. — The draft for 28' W, from 3' single roving = ^^ = 9J. Assuming x the draft change pinion, and 54 the B.E.W., the following equation is obtained : — 54 X 130 X 1 oi . 54 3 X 130 .^ t^ .. • • . X 16 X 1 =^^ • • ^ = 28 >^ -16-- = ^^' ^''^' P^"^°^ The size of rim necessary to obtain the rate of rotation of the spindles, 10,500 + 10 per cent, for loss, may be obtained from the following equation, when X = the size of the rim in inches : — „., X 6 10500x100 ...Q^ 940 X Y^ X ^ = OQ = 11680 940 X 6 1 11680 X 12 X f ~ a; 11680 X 12 X ?- X io ^K in • 1 T>- , .". TTTK T. — ~ = T = 18-65, say 19 inches, Eim 940 X 6 1 ' •' The twist per inch = ^Wx 3-25 = 17-2 Therefore the twist per draw (68 inches) = 17*2 x 68 inches = 1170 Assuming the front roller makes 20y*j- revolutions per draw, and the speed wheel contains x teeth, the following equation contains the value of x, allowing 10 per cent, for slippage : — 4 38 X 35 X x X 19 X 6 _ 1170 x 100 _ ^^11 ^ 20 X 35 X 30 X 12 x § ~ 90 1300 X 20 X 35 X 30 X 12 X f x „nr, ^ i i. i •*• — oTs^i q5 OK iQ ?^ = T = 79*7, Speed wheel 20y\ X 38 X 35 X 19 X 6 1 ^ This wheel being too large, a pair of wheels of suitable size may be obtained from the ratio provided by these change wheels, therefore — driver 30 20 or 7077' say xq driven' " 79-7' '' 53 The gain wheels necessary to give 3 inches " gain " are — 75 64 — 3 3- X TTp; X X = — —, — revolutions of the front roller = 19 4 "^ bO ^ here x = the value of the ^-^ , change wheels driver • ^-^ 75 ,Q, . 60 X 19-4 . „, • • 3| X ^,. X a; = 19-4 .•. x = ^-^ ^r^ = 4-31 60 3*6 X 75 AND COSTS OF YARN 175 Any pair of wlieels witliin the range of size applicable and having this ratio would suffice. .-. 4:31 = say 26 These would give the nearest to that required. The builder wheel = ^^ ^ ^^^ + ^^-^^ x ^' "" ^" = 208, say 21. Note. — The differences in the size of the cop required \vill affect the wheel directly proportional to their areas, and therefore as their diameters^ (squared). Exercise 13. — The draft required to attenuate the 13-hank roving, double, to 80- = ^^^ = 12-3. The ratio of the draft change wheels, x, is found as follows : — 10 Q 130 . 12-3 X IG . ... 12-3 = j^xx .-. — ^3Q- = X = 1-5U „ ,. driven B.R.W. 59 56 53 Katio = -J-. — or — r-^ — = ^^, or ^^, or ^7^ driver pinion 39' 37' 35 The revolutions of the rim shaft per draw — Twist per inch = 3*6^80 = 32*2 „ draw = 32-2 x 68 = 2189 The size of rim, a;, allowing for 10 per cent, for slippage — -.„ X ^6 9000 x 100 10000 x 12 x | ^,^„ = ^^0Xj2X|=— yo— -^-- 750 X 6 -^Q The speed change wheels ratio, x, assuming no pause twisting at the head, and the gain 4 inches ; is found as follows : — 2189x100^1x12 27x17 60-4 .„ ^ , , , „ , X I ^ XXX o^- — 5^ = — i7^r— = 17-8 revs, of h .R, per draw 90 6 X 20 35 X 38 ^f _ 17-8 X 90 X 6 X 20 X 35 X 38 * ~ 2189 X 100 X 0-75 x 12 x 27 x 17 = 0-283 Therefore the only possible wheels within the ranges specified in Fig. 33 60 arej^. Gain. — The revolutions of the back shaft and front roller required per draw respectively, being 3*38 and 17-8, the following equation gives the value of x, the gain change wheel ratio : — 9QQ 75 ,-_ . 17-8x60 .„, 3-38 X g-^ X a: = 17-8 •*•«= = 3-38 x 75 = ^^1 176 COTTON SPINNING CALCULATIONS The pair of wheels within the range specified having the nearest to this 105 gain ratio are tf-, — -. — ^^ r — 1« 15 gain boss wheel The builder wheel = 1^^ + "^-^ x ^^^ 57 2V8 2x8 my 100 X 2 Exercise 16. — The draft required in the rollers = — ^n — = ^^• The draft change wheels ratio, x, must be — -V^,"- X :c = 10 _ 10 X 16 _ 160 •'• ^ ~ 130 130 = V2[ Therefore the suitable draft wheels are — B.B.W . ^ 48 53 54 P.W. ~ 39' 43' 44 The twist per inch required = 3*18^100 draw „ = 64 X 3-18^100 = 2035 Allowing for 10 per cent, loss, the calculated revolutions of the spindles per . . 2035 X 10 ,„oo draw required = „ = ^zdS. The actual revolutions per minute of the spindles required = 8000 ^ , 8000 X 10 .*. „ calculated „ „ „ — g With the size of rim required 570 x ;r7, x -g X 10 X I in.r ••"= 570x6 " = 19-5 say The revolutions of the front roller per draw required = — -^ — = 17*8 ^ r ca ■ X. a 1 ^888 X 10 X | ,,„ The revolutions of the rim shaft per draw = -^^ — -^— ^ = 143 The speed change wheels ratio, x, is therefore — 17-8 X ^"^ X 3^ X a; - 143 x- ^-^^ ^-il^^^ - 1-755 17 8 X ^-^ X g^ X a; - 14d x- ^^.^ x 60 x 35 " ^ '^^ Therefore any of the following pairs of wheels would be suitable : — speed wheel _ 42 44 49 51 rimlhaft wheel ~ 24' 25' 28' 29 AND COSTS OF YARN 177 Gain.— The revolutions of the back sliaft and front roller reiiuired per draw, respectively, being 3-38 and 17-8, the following equation gives the value of x the gain change wheels ratio : — 3-38 X /.iJ X cc = 17-8 X = 4-21 And hence the following pair of these wheels are most suitable — 105 _ gain wheel 15 gain boss wheel + rr, 1 -n 11 12V100 , 12x100 The builder wheel — 2V8 X ^'^^"l - 47 2x8 (\if ~ Particulars of Gearing in *' Dobson's Ord." Mule.— Fig. 34 shows Fig. 34. the arrangement of the gearing in mules for medium and medium fine counts as made by Dobson and Barlow. The following are particulars of the various trains and the range in the size of the wheels shown : — N 178 COTTON SPINNING CALCULATIONS (rt) Train to Sjnndles. — Revolutions of the rim shaft (H G) per minute from 400 to 850 per minute. Eim pulley, D, 12- 22 inches ; tin roller pulley, D3, 10-12 inches ; tin roller, U, 6 inches ; spindle wharves, vi, 3-4 inches. (h) Train to the Rollers.— J, 19 ; K, 58 ; L, 30-56 ; C, 60- 100 ; R, 32 ; S, 25. (c) Roller draft gear : 7c, 20 ; Z, 180 ; A, 30-60 ; m, 30-70. Diameters of rollers : front, 1 inch ; middle, | inch ; back, 1 inch, {(1) Train to the Bach Shaft from the Front Boiler Shaft. — T, 51-55; 0, 55; E, 70-78; P, 16-20; Q, 68; M, 15: N, 55. Revolutions of the back shaft per draw : 3*5 for 64-inch draw ; 3*28 for 60-inch draw ; 3*06 for 56-inch draw. (e) Train for Slow Boiler Turning, sometimes called the Eeceding Motion.— JJ, 20; V, 40; W, 1 ; X, 30; Y, 24; Z, 24. Train for Holler Delivery during the Inward Run. — i, 14-17 ;i, 40. Taking-in and Baching-off Motion Gear. — a, 14 inches ; c, 17 ; /, 24 ; (7, 14 ; h, 40 ; c, 10 ; d, 73. Taking-in motion shaft, a : 170-350 per minute. Revolutions of taking-in motion shaft (/ per 64-inch draw, 3. Building or Shaper Motion. — Wheel, 12-70, and various pitch of screws. Twist Wheel— ^0-120. ExEKciSES. — Ascertain the following, from the particulars contained in Fig. 34 :— 1. The range in the rates per minute at which the spinrlles may be driven. 2. The range in the twist that may be inserted in the yarn. 3. The range in the draft. 4. The range in the counts, twist and weft, which the machine is adapted for in the respect of twisting with the normal twist constants. 5. The ratio in the movement of the carriage before and under the influence of the jacking motion, assuming that during the former movement the drawing- out band is on the full-sized portion of the scroll ; and at the termination of the latter movement, on the half-sized portion of that part. 6. The ratio of the roller and carriage movements during twisting at the head and when in ordinary action. 7. The ratio in the rates of the spindles during spinning and Avhen backing-off. 8. The time, in seconds, taken to move the carriage-in, at the slowest and quickest rates. 9. The length, in inches, delivered by the rollers during the inward run. AND COSTS OF YAEN 179 Answers — 1. 3200-14,960. 2. 7'28-44-5. 3. 4-5-21. 4. 4-0^ twist, 5''-25 weft to 210' weft, 152" twist. In the above calculation, the calculated twist is as obtained without the use of twist wheels. By using twist wheels, the twist may be extended to suffice for all practical rctiuirements, taking the above as representing f of the possible twist then the range could be extended to 78'4 turns per inch. Example in respect of Exercise 5. — The difference in the train pulling out the carnage during jacking : R, S, being in abeyance, and the motion is obtained through M. N. The train prior to jacking, from the side shaft, is E, S, T, 0, E, P, Q ; and during jacking M, N, 0, E, P, Q. mu A-cv • ., 1 32 55 16 , 15 55 16 32 , The difference m these values are ' i^i n7\< fs ^^^^^ rE> ^-n^ po> or, ^ > and 15 ^ respectively, or 3'5 : 1. This is the ratio, when jacking is proceeding, with the drawing-out band wound upon the full-sized portion of the scroll. As the scroll portion is gradu- ally brought into action this ratio increases. When the half-size portion is acting, the reduction in the rate of the movement has attained 3*5 x 2 = 1, of the normal rate. Exam2)le in respect of Exercise 6. — The difference in the trains driving the rollers whilst the carriage is at rest, and twisting " at the head," is as follows : — The wheel train RS is in abeyance, and motion is obtained through train U, V, W, X, Y, Z, and therefore— 32 20 1 24 The values of these trains are respectively .^Z and jr., ^, ^, or as 77 : 1. Example in respect of Exercise 7. — The difference in driving the spindles during spinning and " backing-off " are respectively — Lowest rate of the rim shaft during spinning, 400 .„ 170 X 10 " backing-off,' 73 and therefore the rate of the spindle during the latter period is z.rf7-. ^j^ times less than during the former period = slightly more than ■^. Example in respect of Exercise 8. — Assuming the taking-in scroll shaft makes 3 revolutions per draw of 62 inches, the time in seconds taken to draw the carriage in, is — 3 lowest rate .-„^ ,^^ ^ x 60 = 4'27 seconds 170 X \'i xji or, average rate, 14^ inches per second. 180 COTTON SPINNING CALCULATIONS Example in respect of Exercise 9. — Assuming the back shaft makes 3*39 revolutions during the drawing in of the carriage and the 17 wheel is in use on the back shaft, the length delivered, equals — 17 1" X 22 3-39 X -77. X = — = 4-52 inches Exercises. — Ascertain the production in hanks per 55 hours, without allowances for stoppages ; and the various change wheels necessary to adapt the gearing, as contained in Fig. 34, for the undermentioned counts and conditions of production. Allowances : For slippage, in driving the spindles from the rim shaft, 10 per cent. ; draw, 60 + 4^ inches, the latter delivered during the inward run ; backing- ofif and run-in to occupy 5 seconds ; loss of speed due to changes, 10 per cent. 1. GO W. from 10-hank double roving, Egvptian : actual speeds of rim and spindles, 850 and 10,000 revolutions per minute ; gain, 1 inch ; jacking, 1 inch ; 5 per cent, of twist being inserted after jacking. 2. 60 T. from 12-hank double roving, Egyptian : rim and spindle speeds, 840 and 10,000 revolutions per minute actual ; gain, U inch ; jacking, 1 inch ; 12 per cent, of twisting after jacking. 3. 80 W. from 14-hank double roving, Egyptian : rim and -spindle speeds, 840 and 9000 revolutions per minute actual ; gain, 2 inches ; jacking, 1 } inch ; 8 per cent, of twisting after jacking. 4. 80 T. from 16-hank double roving, Egyptian : rim and spindle speeds, 840 and 9500 revolutions per minute actual ; gain, 2 inches ; jacking, 2 inclies ; 12| per cent, of twisting after jacking. 5. 94 W. from 16-hank double roving, Egyptian : rim and spindle speeds, 840 and 8700 revolutions per minute actual ; gain, 2 inches ; jacking, 2 inches ; 10 per cent, of twisting after jacking. 6. 90 T. from 16-hank double roving, Egyptian: rim and spindle speeds, 840 and 8700 revolutions per minute actual ; gain, 1 inch ; jacking, 2^ inches ; 12^ per cent, of twistmg after jacking. Example of working Exercise 1. — The spindle speed will be attained by using a rim and tin roller pulleys of the following diameter : — Let X = the spindle speed change ratio ; then 860 X . X « = ^-^^ .: . = ^m = 1-634 .'. 18 inches R.P. and 11 inches T.E.P. or, others giving this ratio. The revolutions of the rim shaft per draw must be — GO -h 4i X 3-18 /6U _ . , 18 "6 Tiu ^^^ II ^ V ^ 100 AND COSTS OF YARN 181 The speed change gear must be arranged to obtain the delivery of 60 - 2 inches 3*28 X 59 whilst the back shaft is moving the carriage out 59 inches, and therefore the — -gQ — revolutions of the back shaft are required in the same period. During this move- ment the spindles are required to insert twist in accordance with the state specified, i.e. 100 per cent. — 5 per cent. — x per cent, twisting during jacking. During "jacking " the carriage is assumed to move at f the normal rate, and there- fore requires a period equal to that required to move the carriage 3^ inches at the latter rate. Hence, 95 per cent, of the twisting equals the period required for 59 + 31 inches of movement at the normal rate, and therefore the revolutions of the rim, during the above 59 inches, must be — roi = 8^1 P^^ cent, of 135 = 120 revolutions of rim During the run out of the carriage, the front roller is required to deliver 58 inches, and therefore it must make — 58 1 X -T-- = 18'43 revolutions The speed change gear ratio {x) is therefore — 120 X \% XXX ^ = 18-43 .-. X = ^fon-^f \^^ = 0-366 ^*' -■> 120 X 19 X d2 The speed change wheels, within the range having this value, are — driver 34 _35 36 37 38 39 40 driven lOr 104' 107' 110' 113' 116' 119 3-28 X 59 TJie "gain" change gear must be arranged to impart „^ — revolutions to the back shaft per 18-43 revolutions of the front roller, before jacking commences. Therefore the gain change wheel ratio (x) must be — ,„ ,„ 55 3-28x59 3-28x59x68 ..... 18-43 X .T5 x a; = ^,7:^ /. x = -^~r^ ^^ — ^ - 0-216 68 60 12-43 X 60 X 55 The change wheels nearest to this value are — driver 16 ^ driven 74 TJie draft and draft change wheels, — A 10-hank double rove would necessitate a draft of -^^ = 12, if the draft due to gain and jacking is neglected. Taking the latter into account, it would l)e — 12x621 ^.. 182 COTTON SPINNING CALCULATIONS The draft change wheel ratio (x) to give tlie latter draft must be — -L8^ xx= 11-6 .-. X = ^-^^^^ = 1-29 The draft change wheels, within the range specified, containing this value- driven _ 62 58 53 49 driver " 48' 45' 41' 38 Twist wlieeJs are necessary when the rim shaft is required to rotate a definite amount after the carriage has reached the " head." Usually it is most convenient to arrange them to make one or two revolutions per draw, and therefore, in this instance, since 135 is not available, ip, say G8. rr- 1 135 60 X 100 ^ ,^,, , ,,,, Time per draw = gjQ x — ^-^ — + 5 = 10-15+5 = 15-15 sees. TT 1 • ;ii 1 60 X 60 X 55 X 64^ „„ „ Hanks per spmdle per week = — tttk o^ ottt^ = 27*8 il5-15 X 36 X 840 Examj)Ie of working Exercise 6. — The required speed of spindle will be obtained when the change pulleys in the gear from the rim to the spindles have the ratio x in the following equation : — .*. a = 1-44 .'. ratio = rp p p = 11 nearest Tlierefore the revolutions of the rim per draw, if the latter are adopted— - CO + 4^ X 3-6 X V90 X 100 _ ^.„ 16 w~: — "^^^ zy X ij X 90 Note. — The ^^ is the slippage. The speed change gear must be arranged to obtain the delivery of 60 — 3^ inches whilst the carriage moves 57-^ inches outward, and therefore the back shaft makes 3-28 X 57V' '. pjTT — ^ = 3-14 reA'olutions during this roller movement. The spindles are required to insert twist amounting to the following, in the same period, 210 X 87i X 57- and hence zrj~ ~ revolutions of rim per draw = 159. 100 X 6b| ^ 573 . ^pf is the fraction of 87J per cent, of 210 revolutions, during which time the carriage and rollers are moving at the normal rate. This is ascertained from the rate of jacking proceeding at ^ slower than the normal rate, the jacking rate being from 05; to i the normal depending upon the extent of the scrolled portion of the drawing-out barrels, on the back shaft, in action, AND COSTS OF YARN 183 The front roller is therefore required to make ~, — - - revolutions prior to 1 X --f- ^ jacking, and whilst the rim shaft makes 159 revolutions, and hence the speed change wheels ratio, x, is contained in the following equation :— 159 X >^ X a; X „^ = - — i., = 18 58 2o 1 X --J^ . _ 18 X 58 X 25 _ . " ^ 159 X 19 X 32 " '" The speed change wheels nearest to this value are ,??r '^^^. 111 driven The 111 wheel is beyond the range stated on the figure, but in this case 110 would probably suffice ; if not, it would then be necessary to make an alteration in some other wheel of this train. For values lower than 0-27, the most con- venient alteration is R. The " Gain " Chainje Wheels must be arranged to give 3-14 revolutions to the back shaft whilst the rollers make 18 ; therefore the gain change wheels ratio, X, must be — 18 X tg X cc = 3-14 /. X = ^^^ = 0-216 The " gain " change wheels having this ratio and within the ranges specified 10 are:^^. The Draft and Draft Change Wheels.— A IG-hank double rove will necessi- 90 a draft of ^^ = 11], if allowance Allowing for the latter, it would be — 90 tate a draft of ^ = 11], if allowance is not made for "gaining" and jacking Hi X g^^j = 10-G^ *2 The draft change wheel ratio, x, is contained in the equation — ^A xx = 10-63 .-. X = 1-18 Therefore the draft change wheels suitable are — driven _ 53 59 65 66 driver ~ 45' 50' 55' 56 The time per draw in seconds = | !^ ^ ? ^ l^i^ + 5 = 21-7 840 X 1 X 90 The hanks per spindle per week = ^A^^^'^P^ = 19-5 21-7 X 36 X 840 Mule Calculations. — Figs. 36 and 37 show the gearing as in Piatt's mules. The following examples are taken from those figures. Motor drum, 800 revolutions and 11 inches diameter. Line shaft drum driven from the motor, 38 inches diameter ; for driving the mule, 28 inches. Counter shaft drums : driven, 18 ; driver, 24 ; grooved pulley for T-up motion, 12 inches. 184 COTTON SPINNING CALCULATIONS The revolutions of back shaft for G2i-inch draw = 3i „ „ „ 60 „ = 3-65 „ „ „ 58^ „ = 3-56 Alterations for counts 100' from double 18 hank Sea Islands JRove, assuming the present speed of spindle suitable. The present speed of spindle o^„ 11 X 28 X 24 X 16 X 6 p.-,Q„ _ , ,. . , = 800 X jTTs Tn tt; T^ Q = 6287 "7 revolutions per mmute 38 X 18 X 16 X 11 X f ^ Twist constant = 3-6 ,, per inch = 36 Twist per draw of 62" put up, i.e. 58V' + 3i" = 62" x ^m x 3-6 = 2232 The revolutions of the rim must be such as will give 2232 revolutions of spindle per draw. Assuming a loss of 5 per cent, in transmitting the motion to the spindle from the rim shaft, then the revolutions of the rim shaft per draw should be— 2232 X 100 X 11 X 0-75 ^.^ TT^ — . ^^ = say 202 95 X 10 X b '' The duty of the twist wheel is to control the revolutions per draw of the rim shaft. In this case the twist wheel divided by 2 equals the revolutions of the rim shaft. .-. 2A2 = twist wheel = 101 If there were no gain between the movement of the caftiage as compared with the length delivered by the front roller, then the rollers must deliver, during the outward run of the carriage, 58^ inches, and therefore the front roller must make — ^„ ^,, = 17-518 revolutions, say 17-52 The present gear would deliver — 202 X ,^ 7^ oTs = 30-3 revolutions of front roller instead of 17-52 70 X 60 X 30 Therefore if the change be made at the speed wheel, a — TnTKr, — = 10^ wheel would be necessary. Such a large wheel would probably be impracticable. Usually the driver of the speed wheel is constituted a change wheel, in which case the extent of the dilTerence in the change practicable, in the speed wheel, and that required, would be possible at the driver Avheel. Assuming that up to 90 are the available sizes of speed wheels, then the speed wheel driver would need to contain— ^-^ = 62 teeth 104 AND COSTS OF YAEN 185 N.B, — III such a case it would be unnecessary to use the twist wheel, as the fact of the carriage getting out to the head would control the revolutions of the rim, but less accurately. No Gain. — The gain wheel and its train controls the ratio in the movement of the carriage relative to the spindle. The rollers must necessarily deliver 58} inches, and the carriage must move that amount. The movement of the back shaft in drawing the carriage out G2?,-inch draw is given at 3* revolutions. Therefore, for 58^-inch, proportional movement 34 ^ 531 \vill be required, or — t.^, — - = 3-56, instead of 3-8. 0<iTy Should this be the case, then the front roller must make ^^ — ^— ; revolu- IB -^ 7 tions, whilst the back shaft makes 3-56 revolutions ; therefore the revolutions of the front roller = 17-52. Note.— Variations in the tension and size of drawing-out bands will cause variations in the revolutions of the back shaft per draw. With the present gear the revolutions of the front roller per 3*56 revolutions of the back shaft, are (see p. 192) — 3-5G = / revolutions of F.R. x 20 \ / revolutions of F.R. x 40 ^ V 2 X 60 j "^ I 2 X 40 y (revolutions of F.R. . revolutions of F.R.\ „/. .k __ + 3G X 45 .. ^u^ - ^ 2 / 60 X 90 /revolutions of F.R. 3 revolutions of F.R.\ G •■• 3-^« = \ 6 + 6 J20 • a KR _ '^^ 6 _ 4a3 _ a; ..d-ob_-g X2-Q-20-5 .-. 3-56 X 5 = a; .-. X = 17-80 revolutions of F.R. The gain wheel must therefore be altered to give 17*52 revolutions, and therefore — 3-56 = / 17-52 X 2^\ /17-52 x 40\ V 2 x 60 / V 2 X 40 } 60 G.W. 36 ^ 45 /17-52 , 17-52\_ ,, (^-g- + -2-J36x45 3-56 60 X G.W. 186 COTTON SPINNING CALCULATIONS /17;52 Sx 17-52^ 6 \ 36 X 45 GU X (i.W . „ _ 70-08 3G 45 ..6-bb- ^ Xg-^x^^^,-^ 1 3-56 X 6 X G O 70-08 X 3G X 45 ~ G.W. 70-08 X 3G X 45 G.W. 3-56 X G X GO 1 70-0 8 X 9 ^56^>r2 .-. G.W. = :^v~- = 88-5, say 80 or 88 " " Gain " CImnges. — The 36 gain boss wheel combined with an 88*5, gives, according to previous calculations, a delivery by front roller of 58-5 inches, Taking this as a basis, the amount, in inches, delivered by the front roller per 3-56 revolutions of the back shaft, with various other sizes of gain wheels, is as follows : — Gain boss wheel. 36 36 36 36 36 36 36 36 36 35 34 37 36 Gain wheel. 88 87 86 85 89 90 91 92 90 90 90 90 91 58J X 88-5 88 58-5 X 88-5 87 58-5 X 88-5 86 58-5 X 88 5 85 58-5 X 88-5 89 58-5 X 88-5 90 58-5 X 88-5 91 58-5 X 88-5 92 58-5 X 88-5 90 57-52 X 36 85 57*52 X 36 34 .57-52 X 36 37 56-89 58 83 59-5 60-2 60-9 58-17 57-52 56-89 56-26 57-52 59-16 G09 55-9 Variations in count resulting. 99-5 98-4 97-2 96-0 100-5 101-6 102-S 1040 101-G 99-0 960 104-6 102-8 AND COSTS OF YARN 187 Gain boss wheel. Gain wheel. Variations in count resulting. 35 91 "'=■«!.>'''= 58 31 100-5 34 91 ''■'I'' "" = 6002 97-2 37 01 56-89 X 36 „ „. _ oo-3o 10.-. 8 36 89 5817 - 0-2S ("gain) 100-6 35 89 59-83 + 1-33 „ 97-8 34 89 61-32 + 2-82 „ 95-4 37 89 56-6 - 1-9 103-3 36 88 58-83 + 0-33 „ 99-4 35 88 00-51 + 1-01 „ 90-7 37 88 57-24 - 1-26 „ 102-0 The effect of gain on the counts of the yarn spun (see right-hand cohimn). The EoUer Draft Wheel. — The draft necessary to attenuate two ends of 18' rove, so that it is delivered by the F.R. 100' count, must be — l-^'-lUorXon jLa ~" '•" 'J The ratio in the surface movements of the front and back rollers respectively, must therefore be 100 : 9. With the diameters of those two parts alike, and the draft wheels as given, then the pinion wheel (x) would need to be — lOOo; 9 54^ 140 X 16 100 54 X 140 54 X 140 X 9 ,.T . •• 100x16 =«' = ^2-5 Hence, the wheel used must either be 42 or 43 ; the count in these instances would be 101"1 or 98-8. If the exact count was required, it would be necessary to employ a pair of wheels having a ratio of 7875 : 10,000, Draft Wheels. — Other pairs of wheels, giving a close approximate to ^-p^J*^, are — B.R.W. = 80 75 70 GG 61 56 52 47 Pinion = 63 59 55 52 48 44 41 37 ■Count = 100-0 100-1 100-2 99-95 100-0 100-2 99 88 1000 Exercise 1. — Assuming the spindle speed 6287 revolutions per minute is too slow, and that it is required to be 7073, what changes would be necessary ? — (1) To obtain the desired spindle speed. The readiest way is by increasing the size of the rim — 16 X 7073 ,Q . , . ~ 6287 — ~ lo-mch rira 188 COTTON SPINNING CALCULATIONS (2) To obtain the riglit speed of the carriage and rollers relative to the spindles, it will be necessary to change the speed wheel. Speed Wheel. — If 90 x 52 constitute the driven and driver, change wheels, the speeding of the spindles means that twisting takes place quicker, and there- fore the rollers must be made to deliver quicker in like proportion. . 90 X 16 _ 720 .. , , , . . — .r. — = -q- = oO speed wheel The rate of the production would be the time taken to twist G2 inches of yarn, after allowing 5 per cent, for loss in transmission, with the spindle making 6287 revolutions per minute. rp, ,. . -, , 1 , , ., 22x32x100x60 „„ ,,o Ihe time in seconds taken to twist = ^ -^ ^-= — =22-418 95 X 6 X 287 The time in seconds taken to backing-oif and run in = 4-5 Time per draw = 26-918 The production after changing, i.e. revolutions of spindles to 7074 instead of 6287— rr- + • ,• 22-418 X 16 ,„„^» Time twisting = ^-^ = 19 927 sees. Time twisting backing-off and run in = 4*5 Total time = 24-427 Production in hanks per week of 55 hours, in case of 18-inch rim — 60 X 60 X 55 X 62" ....,, . n 24-427 X 36 X 840 = ^^'^^ ^^''^"^^ P'^' ^P"^*^^' Production in case of 16-inch rim : when the rate of spindle in revolutions per minute with 18-inch rim is — 800 . "JlfS? 24 X 18 X 6 ^,„„ 38 X 18 X 16 X 11 X I and — 60 X 60 X 55 X 62" _ ( production in hanks with 16-inch rim on 26-918 X 36~>r840 \ and spindle revolving 6287 = 15-08 Exercise 2. — A mule making 50' T. has the following change wheels : Draft pinion, 40; rim, 18 inches; speed, 80; builder, 50. What changes in these would alter the counts to 36' with — (a) The speed of spindles unaltered ? (6) „ „ increased \ ? Answers — (a) (b) Draft pinion 56 56 Speed 68 58 Eim — 21 Builder 1 47 47 ' Rule given on p. 1G8 is here used. AND COSTS OF YARN 189 ExiiRCisE 3. — x\. imile containing 1000 spindles and spinning 48', the draw being 62 + 4 inches, and 1100 draws are made in forming a set of cops. Find the weight of the set of cops, allowing 2| per cent, for breakages. A)is. 48 8 lbs. Exercise 4. — The carriage in a mule, producing 46' W., is known to move G per cent, slower than the front roller, single 6-hank rove being used. Find the draft required in the rollers. Ans. 8'17. Exercise 5. — A mule completes 5 draws of 64 + 4 inches each in 68 seconds when spinning 40' T. The time occupied in backing-off and winding is 4|- seconds. Wliat will be the calculated and maximum actual rate of revolutions of the spindles, assuming the slippage and loss of time, due to reversing, is known to be 25 per cent. ? Take the twist standard for American cotton. Answer, TV- 1 68 - (5 X 4i) 46? Time per draw — ^ ^ = ■* o = 9"35 seconds Twist and actual revolutions of spindle per draw = 375,v/40x68 = 1612 Calculated revolutions of the spindle per draw = 3*75v'40 x 68 x ^fP- = 2150 Actual maximum rate of revolutions of spindle "» _ 3-75^40 x 68 x 60 per minute / 9^35 ~ 10620 Calculated rate of revolutions of spindle perj _ 10620 x 100 _ .,070^ minute / 75 ~ lo7-0 Exercise 6. — What would be the production in hanks and pounds, per week of 55^ hours, per spindle, and per mule of 1200 spindles, when the following allowances are made: 8 minutes per doff; 9^ hours for cleaning; 2h per cent, for other stoppages, the cops weighing at the rate of 10 per pound ? Eequired : the twist per inch minus time per draw, and the production in hanks and ounces per spindle, per 55^ hours, in a mule making cops that weigh 10 per pound, and working under the following conditions : Nett time worked, 53 hours ; allow 2h per cent, for breakages ; for doffing, 8 minutes per dofif ; counts, 120' W. from combed special Egyptian cotton, (twist constant, 3-18). Spindles working at two rates of speed — first, 5880, and second, 9000 revolutions per minute. Five-eighths of the twist only is put in at first speed. The backing-off and run in occupies 5| secoads, and the length of the draw is 58i + 3| inches. Answer — Twist per inch = 3-18^120 Twist per draw = 3-18^120 x 62 = 2160 ,,,. , . T 2160 X 5 X 60 2160 x 3 x 60 . ^, Imie per draw m seconds ^ ^^^^^^^ sees, -f- ^^^^^ ^ ^^ ^ + 5h = 13-8 + 5-4 + bh = 24-7 1 ^ 120 X 840 X 36 10 ^ 62 — 190 COTTOX SPIXXIXG CALCULATIONS Time per doff, including dufBng, \ _ 1 120 x 840 x 36 24-7 / " ro ^ 62 ~ m minutes 60 X 60 "^ 60 ^""^' = 40-2 + 0-133 53 X 60 X Doff per week = 971 100 10 120 X 840 X 36 x 24- 7 16 62 x'60 X 60 = 1-22 Weight per week in ounces = 1-22 x \% = 1-95 Hanks per week = -ittt x - - = 14-62 lb 1 Dobson Double Speed and Hastening Motion. — Fig. 35 shows the arrangement in Dobson and Barlow's fine mules for driving the spindles at two speeds. A and B are drums of different size on the line shaft ; these are connected to the counter shaft by belts under control of Line Shaft Counte Taking in Motion Shaft Fig. 35. forks attached to the same bar. The stop rod, operating the straps, is notched to occupy the three positions as follows — (1) Machine stopped; (2) first speed, B strap driving; (3) second speed, A strap driving. This rod is operated in its second and third movements by the movement outward and inward of the carriage. The speed may be changed from the second to the third at any point in the outward run of the carriage, by adjustments. AND COSTS OP YARN 191 The special counter shaft has provision for driving the talang-in motion shaft and also for driving the rim ""shaft. The former has been introduced to displace the friction clutch, driving the taking-in movement, with the view to obtaining smoother action. The latter is for driving the rim shaft at the closing stages of each draw, and to secure more reliable move- Back Shaft Peg release" ' wheel for strap dis- engagement Front Roller Click escapement Clutches Speed change wheels 20 i-Twist I— flpwheel ^"•ix, I25 n-rrH Back Shaft Scroll 36 Change wheels '-'^Tor'gain B.R.W. 1401 20 90 i , 60 1401 - [4^ 30 F.R. Clutch 40 16/ ^20 ^^2 Tin roller shaft Fig. 36. ^ ment of the spindles during that period and extending durin.^ the unlocking of the fallers, thereby controlling the coils wound upon the bare spindle. This latter action is that commonly attributed to motions described as " hastening motions." Piatt Bros. Jacking Motion.— Figs. 36 and °37 show a plan of 192 COTTON SPINNING CALCULATIONS 60 Gain Wheel - •Back Shaft that motion. m{60 - 40) and a (40 - 34) are compound wheels loose on the s^Dindle NX, and they are driven from M and A on the front roller. M is loose on the front roller spindle, whilst A is fastened to it. Movement of NX is therefore obtained from A and M, one- half being expended in turning the wheels with 27 teeth, upon their axes, and causing them to roll upon the two 34. Thus one-half of any motion con- tributed to a or m passes to the T arms of NX. In calcu- lating, the formula is — Gain Bosswheel M36 60,34^ 34 Fig. 37. 2 2 40 X 34 U = to = 40 X 34 20 X 34 60 X 34 Thus, with the front roller clutch closed and making 100 revolutions per minute, the rate of the back shaft would be — lOOt.2 ( 45 X 36 \^( 100 X 1 , 100 X ^ A 1 2V90X60/ V 2 2 ^2 3 2^5 2 ■ 2 = (66|)fo = 20 revs, per minute If the front roller clutch was opened, then the rate would be- 100f.2/'4o X 36\ 100 X + 3 ^ , .. • „, -^(90^r6()) = -^^ ^ To = ^ revolutions per mmute The rate of the carriage during the jacking is thus one-fourth the normal, and in addition that due to the size of the portion of the back shaft scroll in action. AND COSTS OF YARN 193 To find the revolutions of the front roller when the revolu- tions of the back shaft are 3i per draw of 62i-inch draw : Let X = revolutions of front roller. Then — X X 40 X S4: X X 20 \45 X * V2 6ao ■'' 6 36 2 X 40 X 34 ' 2 X 60^90 X 60 ~ "^^ 19 X 10 190 X 6 eao "•''6 5X3' ■ ~ 15 X 4 .-. a.' = -^:;^ = 19 revolutions of front roller In mules not arranged with this motion, the gain wheel is driven by a wheel on the front roller. In Trelfall's Jacking Motion (Fig. 38), the right and left clutch wheels, 130 teeth, are loose upon the shaft ; the central portion 36 Back Shaft 13 T- li5U-p— I 1-. 't i o 11 -'"^^''''^''^^'^''^^'^'^^^ 40 130 Jac mot Clutch > I A in 130- SN\yV\f7V\NV^N'. 70 50- / Gain'Wheel Rim Shaft 148 50 -I— 70 \ (-„ Speed change ^^ wheel Rollec motion 48 plw^^wwjwlvl •": Clutch Front roller I Fig. 38. is connected to the shaft upon a feathered key or the equivalent. The clutch is now shown with the carriage driven at the normal rate. The movement of the clutch towards the back shaft to engage the other 130 part of this clutch, would set the back shaft moving at the slowest rate, namely — 53 X 70 50 X 130 = normal rate 40 X 20 . ,. 7Q ^ ]^3 Q = jacking rate = f;:- the normal = 6-5 194 COTTON SPINNING CALCULATIONS The Losses in Driving in Mules. — The following is an instance of the difference between the calculated and actual speeds of the parts in a mule when the former were made without allowances for losses arising from slippage in the non-positive gearing. The revolutions per minute of the line shaft was 235, and the connection to the rim shaft and spindles, respectively, fa ^ i It' 17'^ X 6 ~i4 VT. The time taken to draw the carriage out to a head 111 X f was 12j sees. The calculated The actual revolutions in revolutions in Loss drawing the drawing out per cent, carriage out. the carriage. Kim shaft 17-2-5 138 = 18-8 Tin roller 263 211 = 24-0 Spindle 1537 2100 = 26-8 Percentage of slippage in driving from : The rim to spindles 8*9 The rim to tin roller 5*2 The tin roller to the spindles . . . 3*93 The loss shown in the third column is inclusive, and repre- sents the extent which the actual differs from the calculated. Deductions. — The allowance in calculating the time taken, and the speed, during twisting, should be about 25 per cent, when the conditions are normal. In arranging the driving gear, from 3 to 5 per cent, should be allowed for each band drive. The losses noticed in belt drives when the conditions are good — i.e. rational sizes of drums and widths of pulleys, and when not reversing — are only very slight, and need scarcely be taken into account. In cases of very high speeds the losses will be greater. Con- siderable variation existed in the loss recorded at different spindles, most probably due to differences in their resistance and in the tension of their bands. The slippage in the gear between the rim and line shaft is only slight when the best systems are adopted. The chief loss is that due to reversing. Further examples of loss in driving mules follow. Particulars relating to the Driving of the Parts in Fig. 35, Dobson and Barlow's Mule for Fine Numbers. AND COSTS OF YARN I95 Revolutions of the line shaft, 235 per minute, actual, Drums on the line shaft, A, 32 inches ; B, 18 inches. Counter Shafts.— The principal counter shaft : C, 20 inches ; D, 20 inches ; G, 12 inches ; E, 24 inches diameter. The auxiliary counter shaft: H, 20 inches; I, 9 inches; K, 15 inches diameter. lUiii Shaft.— Fast and loose pulley, F, 16 inches ; hasten motion pulleys, J, 15 inches; rim pulley, 16 inches (12-22 inches), diameters. rahimj-in and Baching-off Motion Shaft PuUrys.—L, U inches diameter. Sjnndles.— mm, 16 inches; tin roller pulley, 10 inches; tin rollers, 6 inches ; spindle wharves, | inch diameters. Eate of revolutions per minute of : — The principal counter shaft — . , , 235 X 18 first speed, ^ = 211-5 second speed, ~~~ = 376 ^0 The auxiliary counter shaft — first speed, ?5^-2ii§^12^ 126-9 ^ ' 20 X 20 ^ ^ second speed, ?35_x_32j<jL2 20 X 20 "^"^^ ^ The rim shaft— n . , 235 X 18 X 24 first speed, g^ = 317-25 second speed, ?35j^ll2ili = g.. Under the hastening motion High speed, ^MA|2J<J^XJ^ ^ ^ 20 X 20 X 15 -^"^^ Low speed, 235j<J^8j^l2 x 9 _ ^ ' 20 X 20 X 15 ~ ^^ "^ NoTE.-The latter are successively in action at the close of winding. 196 COTTON SPINNING CALCULATIONS The rates of rotation per minute of spindles — ,,, 235 X 18 X 24 X 16 X 6 ,_„ „ , , ^1) 20 X 16 X 10 X l = ^^^^ ^''^ '^''''^ .„. 235 X 82 X 24 X 16 X 6 _„,„ , , (2) 20 X 16 X 10 X ^ = ^^^^ ^^^^^^ '^''^ .o, 235 X 82 X 12 X 9 X 16 X 6 i„oo n t i, i ;i • ^^> 20 X 20 X 15 X 10 X r ^T^ "^^ speed during the action ol the hasten- ing motion ,, 285 X 18 X 12 X 9 X 16 X 6 ^„ ^ a ■, ^ ;■-.* ^^> ' l X20X ^ X15X10X^ = ^^^'^ ^"^ 'P^'^ ^^**°- The Losses in Driving. — Under the above conditions in respect of the gear the actual rates of the spindles were observed to be less to the extent of : (1) 225 per cent. ; (2) 23-5 per cent. ; (3) 18*75 per cent. ; (4) 11*15 per cent. Further, the twist wheel contained 72 teeth, and moved 2 revolutions per draw; during twisting the movement was 140 teeth, and the revolutions of the spindle, in the correspond- ing period, 1454. This shows a loss of 18*8 per cent., the calculated speed being as follows : — 1-^0 X 16 X 6 _ icr>u ~ or 388 revolutions of the spindles more than the actual. The time occupied in making this movement was 12i seconds at first speed, and 8^ seconds at second speed, in these periods the actual revolutions of the spindles being, respectively, 672 and 782. These speeds represent, resjDectively, the following average rates per minute : — 672x60 „,_ ,782x60_.„^„ — TTri — = 3150, and — ^^^ — = 5520 Iz* o'5 The loss of time by the rim shaft, as indicated by the above speeds, is therefore as follows — AND COSTS OF YARN 197 Calculated revs, of rim shaft in 8i sees, at second speed = 80-0 " >' » 121 „ first „ = 67-5 147-5 Thus, 140 revolutions require the time of 147-5, or time lost by the rim shaft = S'OS per cent. _ From this it is seen that 5-08 per cent, of the 18-8 per cent. IS between the rim and the driving shafts, the major portion, Id per cent., being between the spindles and rim shaft. Twist per Iiich._The length wound per draw was as lollows : — Distance moved by the carriage each draw = 59-5" Length del. by F.R. during the run-in of the carriage = 4-5" The approximate length wound = 64-0" Actual twist per inch = ^^ = 22-7 Calculated twist per inch = ^H^ = 28 The actual count spun was 60^ so that the actual twist 22-7 co-efficient = ^ = 2-93, as against 3-62 calculated. The front roller made the following movements each draw :- (1) During the engagement of the F.R. clutch, ] , , ,„ 164 revolutions = o4-6 (2) During the jacking and twisting at the head ) actions, 1^ revolution = 1 (3) During the inward run of the carriage ) 1 revolution ( '^'^" Total length delivered per complete draw = 60-0" Length wound per draw = 64" The total stretching of the yarn per draw is, therefore, 64 - 60 = 4 inches. Of this, the amounts obtained during the above-named periods are — 198 COTTOX SPINNING CALCULATIONS (1) the movement of the carriage being 56" = 56" — 54*6, =1'4 (2) „ „ „ 3i" = 3r-l, =2^ 3-9 Length not accounted for =0*1 4-0 The actual revolutions of the rim shaft after the disengage- ment of the F.E. clutch, i.e. during jacking and twisting at the head, were 73. Therefore the length which should be dehvered by the F.E. during this period, by reason of the action of the slow roller turning motion, is : ^ 73 X 19J< 20 X 1 X 24 X 1,V X 22 ^ .^^^^^ 58 X 40 X 30 X 24 X 7 The actual length observed was 1 inch. The difference was undoubtedly due to the backlash in the motion. Note. — The difference noted in the actual and calculated rates of the spindle emphasize the importance of not relying on the calculated revolutions of tlie spindle unless due allowances have been made for slippage in the belt and band- driving gears. The use of a tachometer is very helpful when arranging the gearing. The particulars given were ascertained, accurately and expeditiously, by the aid of that instrument. Speed Indicators. Losses in the Transmission of Motion, and how Ascertained. — The most convenient mode of ascertaining the extent of losses arising in the transmission of motion is by the aid of a self time -registering tachometer. The ordinary tachometer is defective in that the attachments for connections are imperfect, and in addition the timing has to be done either by a second person or the attentions of the operator divided between the timepiece and the tachometer^ In either case the work is not altogether satisfactory. The illustration (Fig. 39) is of a tachometer, and suitable attachments for spinning machinery. It consists of a recording AND COSTS OF YARN 199 timepiece, D, with minutes and seconds dials combined on the II 4 * m D Fig. 39. left hand. This is fitted ^Yith a fly-back action. The timincr 200 COTTON SPINNING CALCULATIONS commences upon pressure being applied to the recording spindle 2, the centre finger recording from I to 60 seconds, and the lower finger the minutes. The lower projecting milled head is for setting back the minutes finger, and the slight projection on the left hand is the fly-back release for the seconds. The large right-hand deal finger indicates the revolutions up to 100, and the small one on the inner left the hundreds, whilst that on the inner right records the thousands. The projection on the underside of the right dial is the fly-back release for the unit-tens finger, the hundreds and thousands fingers being reset by means of milled heads at the back. F, H, are rubber cupped detachable ends for the spindle of the tachometer. E, and that on the left of centre are rubber pivoted detach- able ends for the spindle of the tachometer. That on the right of centre is a pyramidal recessed end for the spindle of the tachometer. J, K are pyramidal ends for fitting to mule and ring spindles for use in connection with those found on the left and right of centre. This instrument is held by the detachable handle D. In use its great feature is that it can be held in one hand, and with this exception the whole of the attentions of the operator are available for other work throughout the observations. The dials record the results, the range of speed being up to 10,000 revolutions per minute. Length and Hank iNDicATOPtS. Fig. 40 shows the gearing in an indicator for registering the number of draws in mules. The segmental wheel is driven by a worm placed upon the back shaft of the mule (drawing-out shaft). The sector lever, b — hi, secured to a, operates the star wheel c ; to the latter a 3-treaded worm is secured, and this drives the worm wheel d on the spindle ch — f/2. Five dial discs are mounted on this spindle, and these record units, tens, hundreds, thousands, and tens of thousands respectively. Each of these AND COSTS OF YAEN 201 are connected, in sequence, by a train 1 driving a 4, the latter being compounded with an 8, which drives the 20 secured to the next dial. The first dial is secured to di — d2, and the rest are free upon it. Thus this instrument records from to 99999 20, 20, 20, 20. 8, 8, 8, 8, ,4, 4. 4, 4. Fig. 40. draws, the object being to record the work done in a given time for estimating the earnings and for other purposes. The record is exact, as shown by calculation. Thus — 20 X 4 X 20 X 4 X 20 X 4 X 20 X 4 X 10 X 3 8x1x8x1x8x1x8x1x3x1 = 100,000 hanks recorded on the dials by its moving from 00000 to 99999, and then 00000, or one complete revolution of the left-hand dial. Fig. 41 shows the gearing in a hank indicator as used in mules. These instruments are arranged to record the production of the whole of the spindles in the machine, and hence the gear is varied to adapt them for the different numbers of spindles which the mules contain and the length of the draw. In the figure the particulars are of one designed for a mule containing 202 COTTON SPINNING CALCULATIONS 184 spindles only, and making a draw of 58^ inches. It records from up to 20,000 banks, the customary allowance for loss through breakages being 2^ per cent. The action in this case is as follows : — a, rti, a-j, 03, cii are attached, this part is actuated by a worm, X, placed upon the back shaft. By that means a, ai, a^, oscillate, each draw, and the sector lever a^a^^ moves the star wheel h one tooth, h is compounded with c, 30; this latter Fig. 4L drives cl, the 15. d is compounded with the worm c (1), which drives j- (20). f is compounded with the single worm g, and the latter drives h. The lever i, i, is fastened upon the axle of h, and this is loose on the central spindle. At the extremity of this lever is the wheel 21, mounted free on a stud, and its teeth engage two wheels, JcS9 and /40 respectively, k being secured and cannot rotate. /, being free, is moved one tooth per revolu- tion of the lever /, /, upon its centre. The index finger ki is AND COSTS OF YARN 203 attached to I, and this moves in front of the dial indicating from to 20,000 hanks. The length of yarn made, per 184 spindles winding 58^ inches per draw and assuming no loss, per 20,000 hanks registered, _ 40 X 48 X 2 X 15 X 8 X 18 4 X 58V' - 1 X 1 X 1 X 30 X 1 X 840 X 36 NoTK. — 512 hanks = 2^- per cent. = 20,503 hanks Exercise 1. — A mule containing 796 spindles and winding G7 inches per draw has the following wheels stamped upon it, IG x 6 x 3 x 41, and it indicates 20,000 hanks per draw. What percentage does it allow for breakage ? Ans. 3'9G, or 1'4G in excess. Exercise 2.— For what number of spindles per mule would the following 20 20 21 15 3 hank indicators be adopted ? Particulars of their gear, y' ^' y' on' ^' assum- ing the length wound per draw 68 inches, and the indicator to record up to 20,000 hanks. Ans. G8G. Exercise 3. — What number of hanks must be recorded per draw by the hank indicator in a mule containing 1200 spindles and winding 64 + 4 inches per draw, if 2i per cent, is allowed for breaknge ? Ans. 2*63. Exercise 4. — What alteration in the value of the following underhned portions of the gear in an indicator would adapt it for a mule of 1200 spindles, making a 64-inch draw and 4 inches inward roller delivery, allowing 2^ for loss? ,, , ^^, 20 20 21 15 3 Value of the gear, y, ^ , j, ^, ^■ A71S. Present value of the train = 12.600, or number of draws to move the dial one revolution. Piequired value of the train = 7601, or number of draws to move the dial one revolution. Value of the gear required = ;5 — ^ = 5067 oX^ 204 COTTON SPINNING CALCULATIONS Productions ix Mules. Production iu Production in Production in Production in hanks per spindle hanks per spindle hanks per spindle hanks per spindle Count. per 55i hours per 55 hours Count per 55 f hours per 55 hours inclusive. inclusive. iLclusive. inclusive. Twist. Weft. Twist. Weft. 16^-28 32-35 30-34 61 '-80 16-75-19-75 17-20-5 30 31-33 31-33 82 16-5-19-5 — 32 29-32 30-32 84 15-75-19-25 — 34 28-31 29-31 2 86 15-5-19 16-5--20 36 27-5-30-8 28-5-31 88 15-25-18-8 . 38 27-30 28-30-75 90 15-1-18-6 16-19-7 40 26-5-29-5 27-29-5 92 14-9-18-4 — 42 26-29 26-5-29 94 14-8-18 1 — 44 25-5-2S-5 26-28-5 96 14-6-17-75 15-5-19-3 46 25-28 25-28 98 14-4-17-5 48 24-5-27-5 24-5-27-5 100 14-2-17-25 15-19 50 24-27 24-27 110 14-17 15-18-5 52 23-5-26-5 23-5-26-5 120 13-7-165 14-1725 54 23-26 23-26 130 13-3-155 13-5-16 56 22-5-25-5 22-5-25-5 140 13-14-25 58 22-25 22-25 150 12-26-14 — 60 21 •5-24-5 22-5-26-5 160 12-13 — . 62 21-23-5 22-26 170 11-12 64 20-22-5 21 -5-25-6 180 10-11 66 19-5-22 21-24-8 190 9-5-10-5 68 19-21-5 20-24 200 9-10 70 18-5-21-25 19-5-23-2 240 7-2-8-2 72 18-21 19-22-8 260 6-4-7-4 74 17-5-20-5 — 280 5-6-6-6 76 17-25-20-25 18-21-9 300 4-9-5-9 78 17-20 — The Ring Frame.— Figs. 42 and 43 represent the gearing common iu ring frames. A = The back roller and its wheel for driving that on the middle roller. B = The carrier wheel connecting the back and the middle rollers. C = The wheel upon the middle roller. D = The draft change wheel on the back roller. E = The draft change pinion driving the back roller wheel. F = The crown wheel compounded with the draft change pinion and gearing with the front roller wheel. G = The wheel on the front roller for driving the above gear. H = The wheel on the front roller gearing with the train I, J, and K. AND COSTS OF YARN 205 K = The twist change wheel. L = The twist stud wheel, and MN the connecting train from the tin roller shaft. N = The tin roller shaft wheel, this is changed when an extension in the range of the twist is desired beyond that procurable by altering the twist wheel. P, Pi = The tin rollers driving the spindle bands. Q = The spindle wharve. The spindles are arranged in rows on either side. The band indicated by the dotted lines shows the driving when double tin rollers are used for one side only. Fig. 43 shows the driving of the cam W for reciprocating Fig. 42. m V Fig. 43. W the ring rail, the rate at which this is driven controls the pitch of the coils contained by the bobbin. S, T, U, V, are the train of wheels connecting W with I. W produces the reciprocation of the ring rail through the medium of a series of levers, rods and chain connections. The relative positions of their movement is advanced through the agency of a ratchet wheel and a pawl, the ratchet wheel being termed the builder wheel. The number of teeth in the builder wheel and the value of its driving train, S, T, U, V, control the length, and therefore 206 COTTON SPINXIXG CALCULATIONS the weight of yarn placed upon the bobbins. When the rate of reciprocation is insufficient, and other means have been exhausted, the speed of this part is changed by introducing a single, double, or a treble worm at T. The movement of the pawl operating the ratchet is adjustable to the extent of the var3ang sizes of the teeth in the builder wheels applicable. D, E, F, G, are the gear for driving the rollers on the right- hand side, and these are a duplicate of those on the left side. Pi, is the driving pulley connected by belt or rope with the line shaft. The speeds of the spindles in these machines usually range from 6000 to 11,000 per minute, actual. The usual sizes of rollers are from I to 1,^ inch for the front and back positions, and I less for the middle roller ; ^ inch is used for short and 1^ inch for long-stapled cottons. The recognized twist for ring yarns is 4\/count per inch. This is not rigidly adhered to, exceptions being made when it secures better spinning and the amount of the twist has not been stipulated. The Speeds of Spindles. — The circumstances that govern the best speeds of the spindles are : quality and count of the roving and yarn ; condition of the machine ; expertness of the workers. Under the most favourable conditions, a speed of 10,500 revo- lutions actual may be attained with counts 30'-36'. For other counts, under the best conditions, the following revolutions per minute of spindle are given as a guide : — For counts below 30^ — 10000\/intended count VBO For counts above 36* — lOOOOv/36 ^/intended count When the conditions are identical but not satisfactory for the above : For counts below 36* — known satisfactory speed X i/'intended count \/count 875 AND COSTS OF YAl^N 207 For counts above 36^ — known satisfactory speed X v^count -^/intended count With the largest and smallest sizes of the twist change wheels given in Fig. -42, and the spindles making 10,000 revolutions per minute, the speed of the parts would be as follows : — Parts. AVith the smallest change wheels. ^^5'^ "^® largest " change wheels. Tin roller shaft and ) 10000 x ^ _ . machine pulley f 10 ~ ,. , 1, 10000 X I X 25 X 25 ._ .,.-,0 1 rent rollers .... l(rx-T2T^80 = ^^ ^"^ "With rollers of the following diameters, the lengths delivered per minute respectively are — Parts. With the smallest change wheels. Yhfnge wS" T3 X' . „ 7» J- . 57 X ^ x 22 , _„ 228 x Z- x 22 ^.^„ by iront roller, ^ diameter . ^ ^ = lo< ^ = 628 By front roller, 1^" diameter . 203" 812" The twist per inch under the above conditions would there- fore be — Parts. With the smallest change wheels. ^h'ange wS.' By front roller, |" diameter . . . ia§ao ^ (53.7 iaa|<i = 15-9 By front roller, l^" diameter . . . Hggfi = 49-2 itt'l^Q = 12-3 Thus the twist, with the sizes of change wheel applicable and the front roller ^ inch in diameter, ranges from 15"9 to 63'7 turns per inch of yarn delivered by the front roller. This calculation is based on the twist being equal to the revolutions of the bobbin. This is inaccurate when the yarn is unwound from the side of the bobbin, but correct when the yarn is unwound from the ends of the bobbins. To arrive at the actual twist inserted during spinning, it is necessary to deduct from the revolutions of the bobbin, the revolutions about the bobbin made by the yarn in obtaining winding. The different sizes of the twist wheels applicable w'ould therefore obtain the following amounts of twist when the tin 208 COTTON SPINNING CALCULATIONS roller wheel is 25 and the front roller is I- inch in diameter : — Size of twist wheel 25 26 27 28 29 30 ... 35 . , ,. 40 ... 45 Twist per inch . .63-7 61-2 59-0 56-8 54-9 53-0 ... 45-5 . . . 39-8 . . . 35-3 Size of twist wheel 46 47 48 49 50 Twist per inch . .34-6 33-9 33-2 32-5 31-8 The above are ascertained in the following manner : — Eevolutions of spindle per inch delivered by the front roller 80 ., 120 ^ 10" ^ 1 T.W. T.R.W. I" and hence with a 25 tin roller wheel, and a 50 twist wheel, the revolutions of the spindle per inch delivered by the front roller _80 120 10 1 _ -25^ 59 ^I^r^-^-^^^ These results may also be ascertained as follows : — Assuming that the tin roller wheel was 25, and the twist wheel contained only one tooth, the twist per inch would be 63'7 X 25. (This is called the twist change wheel constant number for a 25 tin roller wheel, and the front roller I inch in diameter.) 63'7 X 25 .*. — ^7, = the twist per inch when a 26 wheel is used T.W. constant ,, , . , . , oi'j ^~. — j-T — i — -1 = the twist per mch mtended wheel ^ T.W. constant • i , i .'. ■ ■ , -. — r = required wheel twist per inch ^ When the limit in the range of sizes of twist wheels is reached, they may be rendered again available by altering the size of the tin roller wheel, in the proportion which the range of wheels represent. The limit in the present instance is reached, with a 25 tin roller wheel, when the twist wheel is 50, the twist in the yarn is 31-8 per inch. By adopting the size of tin roller wheel that, together with a 25 twist wheel, will produce 31 '8 twists per inch, the range of twist wheels are again avail- able. Thus — AND COSTS OF YARN 209 63*7 X 25 = the tin roller change wheel constant number for a twist change wheel of 25 teeth .-. — ^^ „ — = the required tin roller wheel = 50 and, therefore, with a 50 tin roller wheel, and with the stated range of t\Yist wheels, the following twists will be obtained ; — Size of twist wheel 25 26 27 . . . 30 . . . 34 35 . . . 40 ... 45 Twist per inch . . 31-8 306 29-4. . .26-5. . .23-4 22-9. . .19-8. . .17-6 Size of twist wheel 46 47 48 49 50 Twist per inch . . 17-3 169 16-5 16-2 15-9 Twist change wheels are usually drivers in the train to the front rollers, and therefore increasing their size increases the length of yarn submitted for twist in direct proportion, and hence the twist is reduced inversely. To change the Counts. — This is done in the same way as in the previous machines — (a) By altering that of the feed. (b) By altering the extent of the attenuation or draft. The results are directly proportional to alterations in either case. Thus : the weight unit of the feed ,, .,. .. f,, ,,. , , ... = the weight unit oi the delivery, and vice versa the count of the feed x the draft = that of the delivery, and vice versa The draft is also determined in the same manner. Assuming, the smallest driver, and the largest driven, of the draft change wheels are used, and the back and front rollers alike in size, then — the draft = §|] X \Pf = 10 Hence, with the back roller wheel 60, the range of pinions, applicable, would produce the following drafts : — Draft pinion 30 31 Draft. . . 10-0 9-65 Draft pinion 56 57 58 Draft. . . 5-35 5-26 5-17 32 33 34 35 . . , . 40 . . . 50 . . . 55 9-37 9-1 8-82 8-57 . . . 7-5 . . . . 6-0 . . . 5-45 58 59 60 5-17 5-08 5-0 210 COTTON SPINNING CALCULATIONS It is thus seen that the fractional change in the draft corresponds with the fractional change in the wheel, and hence large wheels command a finer adjustment of the count, and for this reason the use of small change wheels should be avoided as far as practicable. Whenever the size of pinion required is not available, alter the back roller wheel in the inverse proportion, or change the back roller wheel, altering its size to the extent that will enable the use of the available wheels, as pinions. The following is then the procedure : — Ratio of pinion and back roller wheels, -^. ^-' — '- ; and any ^ pmion two wheels which give a near enough ratio will be satisfactory. Always remember that the back roller wheel has the inverse effect to the pinion, the former affecting the draft in the direct ratio and the latter inversely. The Builder Wheel (Ratchet). — In changing the count, the weight of the yarn is affected in the inverse proportion, so that if the bobbins are required to contain the same weight, then the ratchet wheel must be changed in direct proportion to the count. This is not always admissible in practice on account of the bobbins being filled too full for the rings, through the yarn not being wound sufficiently compact. The rule in calculating the builder wheel is — Builder wheel X count required , , ., , , , = wheel suitable count spun When the size of the empty bobbins are changed or a different size of full bobbin is required, the wheel should be altered in direct proportion to the area of the cross-section of the yarn contained on the full bobbin. The relative area of a cross-section of the yarn = (diameter of full bobbin — diameter of empty bobbin)^. the wheel X area of section of yarn on bobbin required area of section of yarn on present bobbin When the bobbins are insufficiently hard, and the traveller is the heaviest practicable, speeding up the traverse of the ring rail by the most convenient of the wheels S, T, U, Y, will have a beneficial effect. AND COSTS OF YARN 211 Exercises is chaxging the Counts .vnd otukii Coxditioxs of Spixxixg in THE RiXG Frame (Fig. 42). The Froxt axd Back Rollers are takex at I Ixcn in Diameter. EzerciEe numbers. (1) Count of tlie^ yarn | (2) Count of thel rove / (3) Rove, whether single or double (4) Draft . . . (.")j Draft wlieels — F.R.W. . . C.W. . . , P.W. . . . B.R.W. . , (G) Twist per inch . (7) Twist wheels — T.R.W. . . T.W. . . . (8) Twist change! wheels con- 1 staut number ) (;») Revolutions otj spindles per j minute ) (10) Size of empty) and full bob- bins j (11) Builder wheel , (12) Hanks pro-^ duced per 10 hours (no allowances) J 37-5 21 105 40 60 50 ? 79.-) 10,000 f " and 13" -la 40 10 21 105 ? 60 25-3 50 ? 795 50 2 10 21 105 ? 60 ? 25 60 15 21 105 ? 60 31 25 80 20 21 105 •? 57 ? 25 9 9500 9000 8500 8000 30 ? 21 105 ratio 9 50 ? 20 3^ 21 105 40 17-9 50 9 10,500 9000 f " and U" — 1" and k" f " and •? ? ? ? ? ? ? 16 ? 1 5-3 21 105 ratio ? 50 9 8000 f'and If ? 9 Axswers to Exercises. Number of Exercise. Particulars. 1 2 3 4 , S 6 7 8 No. 1 . . _ 1 _ _ 1 _ _ _ •} 10 — 10 — — 5 — ;{ „ 4 . . 75 8 8 8 — 5-72 „ 5 . . . — 35 30 35 35 P. 5 B.R.W. 6 46 P. 50 B.R.W. 53 „ 6 . . . 24-5 28-3 35-8 21-9 — 16 „ 7 . . . 32-4 31-4 56-2 51 44-5 36 44 50 „ 8 . . 1590 1590 1590 795 795 795 „ 11 . . — 38 48 58 49 41-5 27-6 30 ., 12 . . . 81 7-46 6-33 5-45 4-45 95 10-3 16-6 212 COTTON SPINNING CALCULATIONS EXASIPLES IX THE WoKKIXG OF TUE ExERCISES OX PagE 211. 37.5 v^ 2 Exercise 1. — The draft = fg ^ W"! ^^^^ count of the rove = j r. ^ 795 the twist per inch = 4 V count ; twist wheel = ; the hanks pro- , , revolutions of F.R. per 10 hours x circle of F.R. duced = -. — r T — 1 inches per hank 40 Exercise 2. — The draft = j-j~ = 8 ; the pinion wheel (a) is contained in this ,. 60 105 o .1 /• ^ 11 795 . ,, . ,, . equation — x -^ = 8 ; the twist wheel = ^^.^, or, as x in the following ,. 80 120 10 1 or: a .1 1 -n i i 36 X 40 „„ , equation, ^ x -^ x ^ x j ^ = 25*3 ; the builder wheel = — =38-4. Losses in driving the Spindles in Ring Frames. — The following are instances of the observed and calculated speeds of the spindles, together with the losses arising from slippage : — King frame with two tin rollers, one of these being fixed to the machine shaft, and the other driven by the spindle bands. Driver T.R. side. Driven T.R. side. Actual revolutions of T.R 565 555 Actual revolutions of spindle .... 6250 6824 Calculated revolutions of spindle . . . 6460 6342 Percentage of loss 3*25 8*1 The following were recorded after rebanding the spindles on the driven tin roller side, these bands being driven by the driver tin roller : — Driver T.R. side. Driven T.R. side. Actual revolutions of T.R 570 5G2 Actual revolutions of spindle .... 6026 6020 Calculated revolutions of spindle . . . 6541 6422 Percentage of loss 6"67 7*5 The following were recorded in a frame having" the tin rollers connected by an endless rope drive : — Driver side. Driven side. Actual revolutions of T.R 658 650 Actual revolutions of spindle .... 7184 7065 Calculated revolutions of spindle . . . 7500 7430 Percentage of loss 4*2 4*7 The productions in ring frames vary considerably, depending AND COSTS OF YAllN 213 upon the speed of spindles, twist per iiicli,^ strength of tlie yarn, skill of the operatives and their management. The spindles are run at rates as high as 11,000 revolutions per minute, this being exceptionally high, and only practicable under the most favourable conditions. The production ranges as high as 96 per cent, of the calculated when based upon the actual spindle speed. The highest speeds are only practicable with about 36^ to 40^ counts under normal conditions. Productions in Ring Spinning. Actual speeds of Produotiou in Actual speeds of Production in Count. spindles per hanks per spindle Count. spindles per hanks per spindle minute. per 55J hours. minute. per 55i hours. 16 7000-8000 43-51 40 9500-11,000 39-45 20 7500-8500 43-48 50 8500-10,000 31-37 24 8000-9000 42-47 60 8500-10.000 28-34 28 8.500-9500 41-46 70 8000-9000 25-5-30 36 9000-10,500 39-45 80 8000-8500 24-25-5 Productions in Ring Spinning. — In spinning yarns from single roving, with a high draft, or from an inferior or irregular stapled or soft cotton, or in exposed buildings, lower speeds are necessary. The ring spinning machine cannot be as profitably em- ployed in the production of yarns other than the best descrip- tions, when in competition with those produced in the mule spinning machine. Ring frames require better cotton and finer roving for the ordinary classes of yarn. They are principally employed, in this country, in the production of the following yarns : — (1) Yarns containing above the average twist. (2) Yarns made from above the average quality of cotton for the count. (3) Yarns of above the average quality. (4) Yarns which are required in bundle or warp form for the subsequent requirements. In all these, this machine can produce to greater advantage when the counts are within a certain range. ' Sec effects of twists in single yarns, p. 215. 2U COTTON SPINNING CALCULATIONS Twist Standards for Single Yarns. The object in applying twist in spinning yarn is to secure a common bond amongst the fibres, and thereby create a certain tensile resistance to tension. The purposes for which the yarn is required will therefore control the extent of the twist applied. The ordinary standards in use are as follows : — Mule Yarns. — Turns per inch in — V^count X 3*18 = Egyptian weft Y^coun^ X 3'25 = American weft y/count X 3'39 = Egyptian medium \/count X 3*5 = American medium ^count X 3*606 = Egyptian twist ^count X 3"75 = American twist Ring Yarns. — " Soft weft " = Vcount X 3-25 / " Medium weft " = A/count X 3-5 / " Soft twist " = v'^ount x 3*75 \/count X 4*0 = Ordinary twist ^count X 4'2o = Water twist ^/count X 4"5 = Hard twist \ ^couut X 4*75 = Extra hard twist \ v^count X 5-5-9"0 = Crepe The above twists are not rigidly adhered to. Slight modi- fications are made in them by the spinner, such as circumstances connected with the operation of spinning render expedient. A knowledge of the effects of twist, apart from the ordinary standards, is most essential in spinning. The influence wielded by twist varies with the character of the cotton. It is greater in those fibres which are long, uniform in their length, and silky in texture, and well prepared. The shade of the yarn is always darkened with increased application, and the touch is also hardened. A decided curl, or shrink, is also thereby developed. This latter tendency is greatest in yarn which is irregular in diameter or made from harsh cotton. AND COSTS OF YARN 215 Yarns that are highly twisted are less absorbent and colder to the touch, more difficult to dye satisfactorily. Such often become weaker in sizing, bleaching, and dyeing, whereas those less twisted are not unusually strengthened thereby. The Effects of Twist in Single Yarn.— The effect of twist upon the strength of yarn is graphically illustrated in Fig. 44. This diagram was prepared from the breaking resistance of 20' yarn made from Gd. Brown Egyptian cotton. This, in its preparation, had been combed and otherwise most 1 - 2 4 5 6 TWIST CONSTANTS Fig. 44. 10 carefully prepared. In spinning, double roving was used. These abnormal conditions being considered essential for the end in view, as it must be recognized that to obtain the most satisfactory results, such work could only be useful by attaining the best conditions. Yarns were prepared containing twist ranging from 13 to 41-5 turns per inch. In testing their strength the greatest care was exercised to ensure reliable results. Altogether the number of tests made exceeded 12,000. In testing the yarns, considerable difficulty was experienced, 216 COTTON SPINNING CALCULATIONS ill using the ordinary strength testers, with those hardest twisted, and the results obtained were unreliable. Ultimately, the tests were accomplished, satisfactorily, by using the Moscrop patent single thread tester made by Messrs. Cook of Manchester. The whole of the tests, made use of in plotting this diagram, were executed on the same machine. The diagram gives the strength developed in terms of an increasing twist constant, and also in strength per turn of twist. The upper curve shows the former, and indicates the point at which twist ceases to add to the strength, and the lower curve shows that obtaining the greatest value in strength per turn of twist inserted. The inferences drawn from these tests, and from inspection /of the yarn, are — (a) That in the best yarns the strength contributed per turn of twist becomes gradually less at \/count X 3. (b) That in the best yarns the strength ceases to increase with the added twist at \/count x 5. (c) That the shade and touch and tendency to shrink becomes appreciably affected after \/count X 3*5. (d) That the shade is only very slightly affected up to 3'0\/count, and after 5Y/count it becomes very appreciably darkened. (e) A coincidence was that the twist constant realizing the greatest strength per turn of twist was 3'17\/ count. That adopted by the trade generally in spinning weft from Egyptian cotton is 3'18\/count. Twist Standards for Folded Yarn. — The following are the twist constants used in doubling : — Twofolds— XXXX Soft 1-34 XXX „ 1-52 XX ,, 1-8 X ,, 2-2 O.Q }J ^ O Medium 3*39 Common 4'0 AND COSTS OF YARN 217 Lisle .... Double spun . Hard . . . X XX 4-5 5*0 (singles) 5-0 5-4 5-6 Single yarn. Sewings Constant or Co-efpicient. Twofold. Six-cord. As low as possible M^S^^^^^^ ^ constaut ^ 4-5 single constant 6 X constant 6-5 Single yarn. Weft to twist turns Crochet. Twofold. 6-5 Yarns for Fish Xettixg. •Single yarn. Twofold. Common .... / single count \/ number of singles X 4o Six-cord. single count number of singles X 6-5 Kkitting Yarns and Embroidery and for Mercerizing. Singles. Fold. As low as practicable . . / singles \/ number of singles X 30 to 3-25 218 COTTON SPINNING CALCULATIONS The Influence of Direction of Twist in Folded Yarn. The diagram (Fig. 45) shows the influence of the direction of twist upon the strength in the twofold yarn. This figure was plotted from the breaking strains of two series of twofold yarns, one set being twisted reversely and the other twisted in the same direction as that contained in the singles. The 3 4 5 6 TWO-FCLD TWIST CONSTANTS Fig. 45. single yarns used were of very good quality and ah alike, con- taining twist to the extent of 3"6\/count, per inch. The twofold twists, per inch, ranged from 2"5-\/count to 6*85\/count. Those ] twisted in the same direction as the single were harder to the touch and darker in shade, and with the increased twist, their elasticity, to tensile resistance, increased to an abnormal extent. Yarns for elastic fabrics and in preparing for sewing threads have their twist in this direction. Those twisted in the reverse direction exhibited no abnormal features ; a slightly darkening shade was noticeable especially in those fullest twisted. The Influence of Varying Degrees of Single and Folding Twist. — Fig. 4G was prepared from the breaking strains of yarns con- taining a graduated extent of twofold twist, and made from AND COSTS OF YARN 219 single yarn containing the following twists per inch : (1) 2"9, (2) 3-35, (3) 3-9, and (4) 4-5 times the y'counts. The doubling twist was inserted in the reverse direction to that in the singles, and the twofolds comprised 20 differently twisted threads, ranging in extent from v^counts X 2"75 to ^/counts X 5-95. The following were the most noticeable differences in features of these yarns : — Number (4) gave the best strength when containing doubling twist to the extent of 5y/count and below. It was small and pearly. Number (1) was the most attractive yarn, being softest, most 35 TWIST PER INCH 9 10 11 12 13 14 15 16 17 18 19 20 1 ^^ _ - s.^1 . ^ f^ 2^ ^ ^ ^ ^^ X^d r \ 4' r^ y^ / \ _^ ^ / V 3* ' ^ > V ^^ ^* < \ 2- -^ X^ ~1- r*«-i _ 25 —^-^ — 3 4 5 6 TWO-FOLD TWIST CONSTANTS Fig. 46. cylindrical, and lustrous. In point of strength, however, it is inferior to the others, up to 4-9v/counts, turns per inch, but a little beyond this point its strength is superior to the others. Of the four types this would be the most expensive yarn to produce. This figure is useful in indicating the twofold twist most beneficial in variously twisted single yarns; also the most serviceable single twist when a given twist is desired in the twofold. The Effects of Twisting Two or More Single Threads together. — When the twist inserted is in the reverse direction to that con- tained in the singles, it displaces an equal amount from each of them. When the twisting proceeds in the same direction as 220 COTTON SPINNING CALCULATIONS that contained in the singles, that in the singles is supplemented to the extent of the doubling twist. Thus, the former procedure removes the twist in the singles, the fibres being simply re- arranged convolutely, or in what may be termed a spiro-corrugate order. When tension is applied to bodies of fibres so arranged they are pressed towards a common centre, and this force bonds them, preventing the fibres from sliding. It is this change in the arrangement of the fibres, without necessarily changing their compactness, that is responsible for the greatly increased strength of doubled yarn as compared with that of single yarn of a similar weight. The conditions that would have to obtain in order to utilize to the fullest extent the available strength of the body of fibres contained in a doubled yarn, are — That all fibres be equally outstretched and in alignment, so that they mutually share the tension applied. That they are bonded sufficiently to prevent their slippage upon each other and devoid of individual twist. This latter state, in so far as twist is concerned, can readily be obtained. It is in the laying of the fibres equally outstretched that difficulty arises, that state being only partially possible. The formation of the fibres about a common centre, twisted, renders their alignment impossible. The aims of doubling may be stated as follows : — (1) To permanently utilize the available strength of the fibres by preventing their axial movement after the thread is completed. (2) To obtain the desired compactness, lustre, and freedom from ooze, with the fibres bonded in the most suitable manner for the required size of thread. (3) To insure definite elastic properties in the yarn when under tension. (4) To obtain the desired character of surface, such as cylindrical, spiral, corkscrew, pearly, crepe, or other effects. In order to secure the utmost strength, and at the same time prevent axial movement, the twists in the successive stages should be arranged so that they balance in the completed yarn. AND COSTS OF YARN 221 Compactness is the result of tension and compression applied during doubling. In order to obtain the smallest thread from a number of others, as, for example, in sewings and kindred 3'arns, the following procedure is most effective : — In doubling the singles the fibres should be compressed to their limit, by twisting in the same direction as the singles, and to the extent necessary to obtain a balanced state when the final twisting is completed. Thus, when the final twist is great, that in the folded singles must also correspond. In the substitution of the preparing by the final twist the consequent extending and expanding tendencies are fully absorbed, or counteracted by their greater radius about a common centre. Lustre is affected by the angle which the fibres make with the completed thread. It is greatest when they are in line with the axis of the individual singles, and vice versa. Thus, lustre indicates the extent of the twist in the singles and in the fibres. Freedom from Ooze. — This is in the main the result of the rolling action of the yarns against each other in the course of twisting. The Tendency to Stretch, under tension, is regulated by the angle of the singles or strands comprised in the final thread. The more numerous these are the less their stretching tendency. Thus, highly elastic doubled yarns are composed of the fewest singles and strands. The number of strands that can be satis- factorily bound in this way are limited, and hence they seldom exceed four. Above this number the singles or strands have insufficient adherence, and hence plaiting is resorted to. Cylindricity is developed most effectively when the singles are only slightly twisted and of the best quality. Pearly Effects are developed by employing highly twisted singles. Crepe by twisting in the same direction as the singles, also by inserting considerable twist in the reverse direction to that in the singles ; but the effect is not the same in both cases. Spiral Effects are obtained by slight folding twist. Where a small yarn with hard effects are required, highly twisted singles are necessary. For soft effects similar to those 222 COTTON SPINNING CALCULATIONS required in yarns for mercerizing, the singles should be softly twisted. Corkscrew Effects are obtained by doubling — (a) Yarns in unequal tension. (h) Yarns unequal in size. (c) Yarns containing unequal twist. (d) Yarns twisted in opposite direction. The Relative Resistance of Yarns to Twist. — Assuming the CO- efficient of resistance to the first twist in a given length of yarn to be 1, and the resistance, as the twist progresses, directly proportional to the twist contained, the relative resistance, when the diameters of the yarns are not alike, being proportionate to their diameters cubed— then, upon these assumptions, the relative resistance of a body of untwisted fibres, equal to 60^* and 40* yarns, are respectively — When the fibres are twisted, their resistance, when t denotes the twist contained in them, will be respectively — .(iYand^(4=f V\/60/ \v'40/ The above are based on other conditions being equal. The relative resistance of 60' and 40^ yarns containing twist to the extent of 3*5>/count, is therefore expressed as follows : — 60% 3-5v/6o(-^y=-057 40% 3-5v/40(-^y=-0837 When folded threads are required balanced, namely, without tendency to twist or untwist, it is necessary to insert twist to the extent that will balance the forces they contain. Thus, a yarn composed of several single threads should be twisted so that the force developed by the doubhng twist is sufficient to counteract those still contained in the singles. When a number of singles AXD COSTS OF YAEX 223 are bound by twist in tbis manner, the twist inserted adds to, or reduces, that in each single, to a corresponding extent. This action reduces or increases the force which the singles exert. Therefore, when the doubling twist is inserted in the reverse direction to that in the singles, and to the extent of rendering the opposing forces equal, the yarn is then in a state of equili- brium or " still." The amount of twist, which is required to produce the still or balanced state, will be governed by that con- tained in the singles and also by the number of threads comprised in folding. Hence, the more numerous the twists in the single and the fewer the folds, the greater the amount of twist required in doubling the yarn. The extent of the twist required in folding yarns to balance that in the single yarn may therefore be ascertained in the following manner : — Let ci = the count of the single. 0-2= ,, ,, folded yarn. Ti = the twist in the single yarn. T2 = ,, required in the folded yarn. The relative twist required to develop a balance of the forces in the completed thread, when twofold, is as follows ; — The force in the singles before folding is : 'Hvm The force due to the twist remaining in the singles when doubling is completed is : 'b'^ - <37)1 The force due to the doubling twist in the thread is Therefore, the forces in a balanced thread are : 224 COTTON SPINNING CALCULATIONS The above formula, when applied to twofold 50* with ti = 3"5\/ci, gives the following results : — t.2 = 10-9 This method of ascertaining the twist is applicable to all kinds of yarns. It enables that necessary, in the singles, to balance a certain folding twist to be ascertained, or vice versa. Adherence to this method would necessitate considerably more twist, in the single yarn, than it is customary to apply, and hence it would increase the cost and this without commensurate return. In certain classes of yarns it is applied to some extent. The application of the above formula is further illustrated by the following example : — Let the count of the single be 50, and twofold is made containing the usual turns ^^2 X 4 = 20. "What twist would be necessaiy in the singles in order that the completed twofold be in perfect balance ? .•.[(x,/60-20)(-.y> = -^ _ , 20 V50y J V25 a;V50 = 46-5 X = 6*58, the single twist coefficient or constant The Eixg Doubling Fra^te. Fig. 47 represents the gearing common in ring doubling frames, A, Ai being the rollers, and L the driving pulleys, J the tin roller, and I the tin roller shaft wheel, the train I, H, G, E, El, D, Di, Ci, B, and Bi, being the trains of wheels con- necting the front rollers to the tin roller. K and K are the spindles. The following twist is obtained when the smallest sizes of the change wheels are employed : — The revolutions of the spindle per one of the roller, with the smallest sizes of change wheels, are — AND COSTS OF YARN 225 75 X 60 X 120 X 8 20 X 20 X 20 X IJ = 480 and therefore the twist per inch inserted in the yarn, on the left side of this machine, would be — lii V 22 = 87-27 whilst that on the right side would be — 480 21 X -^^ ~ ^^ The range of twist with 20-60 the available sizes of top Fig. 47. change wheels, when the tin roller and the lower twist wheels are both 20, is — On the left side, from 87-27, to 87-27 X §!] = 29-09 ■ On the right side, from 61, to 61 x fB = 20-3 With the available sizes of wheels for G, when the tin roller wheel is 20 and C is 60, the twist per inch procurable, ranges from On the left side, from 29-09, to ^^'^^ ^ ^^ On the right side, from 20-3, to 60 20-3 X 20 60 = 9-69 = 6-77 226 COTTON SPINNING CALCULATIONS With the tin roller 40 and the other change wheels 60 and 60, the twist would be — On the left side, ^n = 4*89 twist per inch On the right side, j^ = 3-38 twist per inch r„, , ,. .. » ,. revolutions of spindle (actual) The production per unit of time = -1—^-, — ■ — r^ ' ^ twist required = inches per unit of time Therefore with the spindles making 8000 revolutions per minute (actual), and the counts 2-72* and twist coefficient 1'5, the rate of production in hanks and ounces per spindle per 10 hours, no allowances, would be — 8000 X 60 X 10 = revolutions of spindle per 10 hrs. 8000 X 60 X 10 . , • ;n • 1A 1 =^^ = inches per spmdle in 10 hrs. 8000 X 60"x 10 , • ;ii • iA I = = yards per spindle m 10 hrs. 4-5 vZ-'g- X 36 -" 8000_x 60 x 10 ^ j^^^j^g , ^ .^^^^ .^ jQ j^^.g^ 4-5 ^/l^- X 36 X 840 8000x60x10x16 ^ ^^^^^^ .^^1^ .^^ 10 1^^.^ 4-5 V^X 36 X 840 X ^2_ This is assuming the yarn does not contract. = revolutions of the roller per 4-5 \/^2- X If X ^ minute on the left side = revolutions of the roller per 4-5 x/^2. X 2i X -2^ minute on the right side "With the particulars of the frame as given in the figure, the different top change wheels that would be applicable, in order that the same turns may be put in the yarn made on both sides of the machine, are as follows : The ratio of these change wheels, left to right, should be as ^ : 1^, or 10 : 7, or 1 : 7. The following exercises are based on the conditions obtaining in Fig. 47 :— AND COSTS OF YAKN 227 Exercises 1. What size of wheel Bj would give twist identical to that on the left side with top change wheels 20 ? 2. Assuming B, and B 107 and 75, respectively, with the top change wheels C, Cj alike and G, 60, whilst the yarn doubled is 2-60' ; what sizes of G would be suitable for iising 2-70', 2-80% 2-90", the same twist coefiScient in each instance ? 3. Assuming the tin roller wheel 20 and bottom change wheel G 20, what size of C and G^ would be necessary for 2-120' on both sides, the twist constant being 4'5 ? 4. Assuming that 2-120', containing 35 turns per inch, is being doubled on both sides, at what rates per minute should the rollers rotate ? 5. What twist per inch would be inserted when the 2^ -inch roller is observed to make 1 revolution per 70 of the spindle ? 6. If the twist is 8-0 turns per inch with a 60 lower change wheel, what size of wheel will give 2-4 turns? Also, at what rate must the roller rotate per minute in both instances, assuming the spindle makes 600 revolutions per minute ? 7. The top and bottom change wheels are 60 and 40 respectively, and the present twist is 24-8 turns, but 25-8 are required : which change wheel would alter to get the nearest to this, and what size of wheel would be necessary ? 8. If the twist per inch was 24*8 and the top and bottom change wheels, 60 and 40 respectively, are each changed for wheels three teeth less, what would be the alteration in the twist ? 9. Give several sets of top and bottom change wheels which would give identical twists to those obtained with : 20 top and 60 bottom, 21 top and 56 bottom. Changes in the sizes of the tin roller shaft and bottom change wheels, affect both sides equally. Alterations in the twist by means of the top change wheels must be made, on both sides, inversely to the changes in the twist required. The rate of the production is altered, by changes in any of those wheels, in the direct proportion to the alteration. When changing counts of yarns, and the twist, required, involves the same twist coefficient, then the sizes of the wheels required are inversely as the v'counts. Thus, if changing from 2-30' to 2- 40% prese nt wheel : required wheel : : v^intended count : V^present count. When the wheels required for carrying out the change desired at one or two of these points are not available, the results desired may be obtained by changing at the other points in the same proportion. The speed of the spindles applicable for various counts 228 COTTON SPINNING CALCULATIONS range from 3000 to 8500, according to the class of work. When changing, ahvaj^s consider whether the new circumstances will admit of or require a change in the speed of the spindles. Such is made by altering the frame shaft pulleys or their drivers, whichever be most convenient. Slippage in Doubling Frames. — In doubling frames there is usually considerable slippage in driving the spindles from the tin roller, and this often results in undesirable variations in the twist which the yarn contains. An idea of the extent of this is contained in the following observed speeds in a ring doubling frame in good working condition. This frame contained one tin roller making 838 revolutions per minute and 8 inches in diameter, the spindle wharves being 1^ inch in diameter. The following were typical records of their speeds per minute : 5186, 5100, 5416, 5265, their calculated rate being 5950, and hence the loss was 12*8, 14"3, 9"0, 11*5 per cent, respectively. This is when neglecting the size of the spindle band. It will be noticed that when the size of the spindle band is allowed for in this instance, the loss will be almost «?7. The Twiner Mule. — Fig. 48 contains particulars of the gear for driving the spindles and drawing-out scroll shaft in a twiner. Fig. 48. N, N are the strap driving the rim pulley M ; L is the rim pulley, and LK the rim band driving the tin roller pulley J, K being the rim band carrier pulley. The tin roller B drives the spindle wharve A ; C and Ci are the tin roller wheels, shown in two sizes, for driving the train D, E, F, G, H ; H is the drawing-out shaft clutch wheel. The other particulars of the above gear are AND COSTS OF YARN 229 as follows :— Revolutions per minute of run shaft, 770. Rim L, 12-24 inches ; B, 6 inches ; J, 11 inches ; A, i inch diameters respectively. C and Ci, 15 and 25; D, 80; E, 20-40; F, 90; G, 15; H, 68, teeth respectively. H makes 3;]^ revolutions per draw in moving the creel out 72 inches. The twist change wheels are : the tin roller 15 and 25, and the wheel E 20 to 40. The rim pulley is seen, on inspection of this gear, to be the medium for adjusting the speed of all the productive parts, and the twist change wheels for altering the rate at which the yarn IS introduced to the twisting influence. If the examples relating to the spinning mule have been understood, the following calculations will be understood. Hence only one example is given in each set of these calculations. ExEKCiSE 1 -Calculate the revolutions of the spindles per minute with con- secutive sizes of riras ranging from 12 to 24 inches in diameter. diaiSter'''~'^'''°^"^'°"' ^''' """'"^^ °^ 'P'^^ ''''"' ^^'^ ''"^ '^ ^- '"<^^^«^ "^ 11 X i Size of rim . 12" 13" U" 15" 16" 17" 18" 19" 20" 21" 02" 93" oi" Revs.ofspindle|5760 6720 7680 8640 9600 10,560 "^ 11^520 permmute / 6240 7200 8160 9120 10,080 11,040 chan^rSstTStst^^ ''' '^''' ''' ''''-' '-'^^ ''' ^'^'-S-^ ''-^^- ^^-^ ^^Emmj^Ic-Beyolntions of spindle per one draw and per 3f| revolutions 3iix 68 X 90x 80x 6 , . lE~x~W^<r25x^^ ~ l-*^^ "^'^'^^ °^ ''- inches .-. the twist per inch = ^ 58 x 68 x 90 x 80 x 6 x 8 _ 68 X 15 X 40 X 25 X 72 X 7 ~ ^ When the tin roller wheel is ^ 25 and the twist change is/ ^^ ^^ ^^ 37 36 35 34 33 32 The twist per inch is / ^'^'^ 12-7 1.3-4 14-3 I 11-8 124 13-05 13-8 147 31 30 29 28 27 26 25 24 23 22 21 ^o 15-7 16-8 18-1 19-6 21-4 03- x 15-2 16-2 17-4 18-8 20-5 22-4 { Exercise 3.-Calculate the twist change wheel that will give the nearest to 23 5 turns per mch when the tin roller wheel is 15. 230 COTTON SPINNING CALCULATIONS ExEKCisE 4. — Calculate the twist per inch with consecutive sizes of twist change wheels ranging from 20 upwards, with the tin roller wheel 15. Alls. Twist change wheel . . 20 21 22 23 ... 30 n, • , -1 / 37-5 34-2 Twist per inch. . . (3^.^ 3^.3 ^6 3 , 258 X 68 X 90 X 80 X 6 X 1 ^^ , Jiixamine. jr^ ^-= ^77. ^-^ ^-5 -_ = 39*4 ^ 68 X 15 X 20 X 15 X 72 X I Exercise 5. — If the twist change wheel 35 and the counts doubled 4,"', what sizes of wheels would be required for 4f-', -"o"-', ^', -^"-% 1^^', when the same twist constant is used ? 35 V^^- Example. — -=^ = wheel suitable for ^\!^' ExERCiSE 6, — Estimate the production in hanks per spindle and in pounds per twiner of 1000 spindles per 10 hours ; the spindles to develop a speed of 11,000 revolutions per minute, and baching off and winding to occupy 5 seconds ; the counts doubled are ^Q-', -"f-', 5^', ^% "#', i^^-^% and the twist constant 4-5 is used. Allow 15 per cent, for loss of speed during twisting, and 15 minutes per doff, the cops weighing 2 ozs. each. Example. — 4f-'. /4-5a/-^*x72\ 100 Seconds taken twisting per draw = I — ti-aaa /^O -of- = 10-04 seconds Seconds per complete draw = 10-04 + 5 = 15-04 Time to make a cop in seconds = — "^^ ^^^ = 15-04 seconds ^ 72 X 85 The above numerators = contents of a cop in inches Time taken to make a cop and) _ 1 x 25 x 840 x 36 x 15-04 15 doff in hours / ~ 8 x 72 x 60 x 60 60 = 5 hrs. 29 mins. + ~ hrs. = 5-733 hrs. bO 10 X 2 X 25 .'. production in hanks per spindle = K:noo tc. f = ^'45 .". i>roduction in pounds per twiner = ^.-^ =218 lbs. Changing the size of the rim affects the speed of all the parts concerned in twisting and introducing the yarn, and there- fore alters the time occupied, in making this movement, in direct proportion ; the time taken to back off and wind remaining unaffected. Changing the twist change wheel alters the twist through affecting the rate of movement of the carriage, in the direct proportion to the change made in the wheel. This alters the AND COSTS OF YAPyN 231 rate of the carriage movement inversely to the twist, the pro- ductive rate being affected in the proportion which this altera- tion affects the period of twisting. ExAMPLK.— Assuming a draw is made in 15-04 seconds, when the twist change wheel is 35, and of this 5-0 seconds is the time occupied in backing off and winding ; the following alteration would arise in the event of employing a 23 twist change wheel : — 10-04 X 35 . . 20 ~ ^^^^ ^^^ seconds occupied in twisting /. time per draw = 17-57 + 5 - 22-57 The rate of production is therefore altered in the terms of 15'04 : 22-57 = 0'666, and not in proportion to the change in the wheels, 0-657. Costs of Yarn. The following are given as representing about the average costs of the various items of expenditure in South-East Lancashire mills in the production of mule yarns of medium count from uncombed cotton when spun from single roving : Cost in pence per spindle per annum. Banding — Twine — Rope 0-5 Carriage on cotton and other materials 2*3 Coal 3-75 Taper 0-15 Cleaning cloths — Engine packing — Brushes 0*25 Leather and cloth for rollers 0-5 Belting and its accessories 0-25 Lubricants 0'9 Repairs : Mill buildings — Machinery and upkeep : basis ) 1| per cent, at 24s. per spindle per annum j' Gas and water l-O Rates and taxes 2-0 Stationery — Telephone — Exchange — Railway tickets — ■! Stamps — Printing and sundry office expenses J Sundry stores 0-5 Insurance 0-45 Interest at 5 per cent, at 25s. per spindle 15-0 Depreciation at 4 per cent, on 24s. per spindle .... 11-52 Wages 360 80-64 Percentage of wages to other expenses ... 45 232 COTTON SPINNING CALCULATIONS In order to ascertain the cost of producing yarn wben the production and the inclusive expenses per spindle are known, the following is the course usually followed : — To the cost of the cotton at the card delivery add the cost of production, per pound, and deduct the sum received, per pound of yarn spun, for the waste. The rate of the production per spindle in the South-East Lancashire district does not vary considerably. The range is given on p. 204. In costing it is usual to disregard the loss arising from waste after the card, because this item is about balanced by the regain in conditioning. The value of the waste is assessed at 2^ per cent, of the cotton price ; this is considered a fair value. Example of the cost of 28" T. made from Middling American cotton at 6d. per pound. Cost in pence per pound. Working costs per spindle per annum SOGi \ Production per spindle per annum, based on 50 „.;, k^ [ = 1-413 working weeks per year and 32 hanks per week " „ — Cost of the cotton delivered at the card delivery, allowing 10 per cent, for loss, ^ — "'"' 8-083 Less value of the waste 0-15 ,, cost of raw cotton 6-0 6-15 Nett cost of spinning 1 -933 Add : cost of selling and discounts 3i per cent on selling price. Example 36' T. from F. Middling American cotton at Q-Wd. Production, 30 hanks per spindle per week. Cost in pence per pound. Working costs per spindle per annum, 80-64 ^ _ 80*64 x 36 _ -i.qok Production per spindle per annum, 50 x 30 hanks / 30 x bO Cost of the cotton at the card delivery, allowing 10 per cent, loss 6*844 8*779 Less value of the waste 0*154 „ cost of the cotton 6*16 6-314 Nett cost of spinning 2-465 AND COSTS OF YARN 233 Example 60' T. Fair Br. Egyptian at dd. per pound. Working costs per spindle per annum 80'64 Production per spindle per annum |^ X 50 Cost of the cotton delivered at the card 10 per cent, wasted, ' — ^t, — Cost in pence per pound. = 4-032 10-0 14-032 Less value of the waste 0*225 ,, cost of cotton 00 9-225 Nett cost of spinning 4 807 The Approximate Costs of Yars when Spun from Single Koving, the Basis BEING 8064 Pemce Cost per Spindle per Annum = 161 Pence per Spindle PER Week. t- a> <» 1 a> <D ^ ^tn 1 °.S fcoS CO "(G a a° II la =3 OJ P.5 "-I. Count and description of yarn. at .2 c II ■3-0 2 & Suitable cotton and grade. Price of cotton at t of compilatio =1 ■ ?^ S " If " 3 a-a l§ *" is Jl II •a s P 1 ° to o ■£ s o o Prime cost of yarn i per pound. Margin between cost of yarn and the raw cotto 1 ^ G.O. American! 16 W. 34 , /G. Broach > 2\G.Tinnevelly) 5-55 12 6-31 0137 0-76 6-933 1-383 16 T. 34 G.O. American 5-71 12 648 0-142 0-76 7-098 1-388 16 T. super. 33 s.L.M. „ 5-95 11 6-68 0149 0-783 7-314 1-364 20 T. 34 b. 5-86 11 6o8 0147 0-95 7-383 1-523 20 W. 34 G.O. 5-71 12 648 0142 0-95 7-288 1-578 24 T. 34 s.L.M. ,. 5-95 11 6-68 0149 1-14 7-671 1-721 24 W. 34 f.G.O. 5-81 12 66 0145 114 7-595 1-785 SOT. 32 b.M. 605 11 6-8 0-151 115 7-799 1-749 30 W. 32 s.L.M. „ 5-95 11 6-68 0-149 115 7-681 1-731 32 T. 30 M. 609 10 6-77 0-152 1-72 8-338 2-329 36 T. 29 f.M. 6-2 10 6-9 0-155 2-0 8-745 2-545 36 W. 31 b. 605 11 6-8 0151 1-88 8-529 2-524 40 T. 28-5 G. 6-31 10 70 0-158 2-20 9-102 2-792 42 W. 28-5 8. „ 615 10 6-83 0154 2-38 9-056 2-906 50 T. 26 M.F. 6-55 10 7-28 0164 3-1 10-216 3-666 50 W. 26 G.M. 6-31 10 7-0 0-158 31 9-943 3-633 GOT. 23 j Special select I grades only 60 W. 24 M.F. American 6-55 10 7-28 0-164 403 11-146 4-596 In those spinning mills preparing the yarn from double roving, at the spinning machine, the cost of the working expenses are 234 COTTON SPINNING CALCULATIONS greater than those previously given. This has been ascertained to approximate VI 2(1. per mule spindle per week. Thus, 50^ T. from double rove, and produced at the rate of 25*5 hanks per mule spindle per week, will cost in working expenses — 1 -72 X 50 „.^_ , ^ — ^^ — = 3"37f<. per pound and 60' T. at 23*5 hanks per spindle per week — 1-72 X 60 23-5 = A' -id. per pound The AppiixiMATE Cost of Yarn spun from Double Eoving as per Data PREVIOUSLY GIVEN. is o -o ai <U 1 .3 c t-> a lid a, a cu . t . ■"SS . 13 U IM □ ^ 0! B CO ^ 0) >> 12° Count and description of yarn. 5| as, Suitable grade of cotton. ^ .2 c a o r:; 8S »*- o o a 0. 2 => If o2? 13S-§ .£"S 1 p. Jog ■3-Ss a; M SI P. 9 1 CM ( 0^ ° S V 2 PM S^2 1 G.O.American 16 \V. 34 , /Broach G. > * \Tinnevelly G. 5-55 12 6-31 0137 0-80 6-978 1-428 1 16 T. 34 G,0. American 5-71 12 6-48 0142 0-805 7-143 1-433 16 T. super. 33 8.L.M. „ 5-95 11 6-68 0149 0-83 7-361 1-411 20 T. 34 b.L.M. „ 6-86 11 6-58 0147 1-01 7-443 1-583 20 W. 34 G.O. 5-71 12 G-48 0142 1-01 7-348 1-638 24 T. 34 s.L.M. „ 5-95 11 6-68 0-149 1-22 7-75 1-8 24 W. 34 f.G.O. 5-81 12 6-6 0145 1-22 7-675 1-865 SOT. 32 b.M. 6-05 11 6-8 0151 1-61 8-209 2-209 SOW. 32 s.L.M. „ 5-95 11 6-68 0149 1-61 8-141 2-191 32 T. 30 M. 6-09 10 6-77 0-152 1-84 8-458 2-368 S6T. 29 f.M. 6-2 10 6-9 0155 2 35 9-05 2-875 S6 W. 31 b.M. 605 11 6-8 0151 2-0 8-65 2-6 40 T. 28-5 G.M. 6-31 10 7-0 0-158 2-41 9-252 2-942 42 W. 28-5 s.M. 615 10 6-83 0-154 2-53 9-206 3-056 50 T. 26 M.F. 6-55 10 7-28 0-164 3-31 10-426 3-876 50 W. 26 G.M. 1 Peeler, Baders,! 6-31 10 7-0 0-158 3-31 10-152 3-842 60 T. 23 JBoweds, or super > I Orleans or Texas) — 10 — — — — 60 T. super ( Ditto (double j \ rove) j American. 60 W. 24 M.F. American 6-55 10 7-28 0-164 4-03 11-416 4-866 50 T. 25-5 Egy. G.F. 9 11 101 3-37 0-225 13-24 4-24 50 W. 26'5 U. Egy. F. 8/5 11 92 3-25 0-204 12-25 4-07 60 T. 23-5 Egy. G. lOJ 10 11-25 4-4 0-253 15-40 5-27 60 W. 25 U. Egy. G.F. 9fB 11 10-3 4-13 0-229 14-20 5-02 TOT. 20-5 j|Egy-G. ) \i „ F.G.F./ lOi 10 11-53 5-88 0-259 17-15 6-77 AND COSTS OF YAKN 235 ■i- , J P4 <a *■§ •K 3 5-S p< . 0. • ^8^ Count and description of yarn. S Suitable grade of cotton. as •o . §1 sa ble percentage up to carding h f the cotton pas ding head per po ated value of made up to and iided in carding. S 3 13 cost of yarn s pence per pounc n or difference the price of the d prime cost of y 1 s II Cost the car Estim waste cl ^1 §-2 III TOW. 22-5 U. Egy. F.G.F. ^ 10 11-0 5-35 0-247 1610 6-22 SOT. 18-5 Egy. G. ni 10 12-5 7-44 0-281 19-66 8-41 SOW. 19-5 U. Egy. G. 10^ 10 11-36 7-05 0-253 18-16 6-29 90 T. 17-0 Egy. F. 111 9 1305 9-1 0-297 21-85 9-97 90 W. 190 U. Egy. F. lOi 10 114 8-15 0-256 19-30 905 100 T. 15-0 Egy. F. lOi 10 1305 11-4 0-297 24-22 13-34 Combed Qua lities — Cost of cot at the com head. * * SOT. 19 Egy. F. 111 10+18 16-4 / 7-25 1 + 0-9026 2951 +1-07 / 23-1876 11-3151 90 T. 17-5 " Hi 10+18 16-4 f 8-85 1+0-9026 0-2951 +107 / 24-7876 12-9151 100 T. 16-0 >» Hi 10+18 16-4 / 10-75 1+0-9026 0-2951 +1-07 / 26-6876 14-8151 The plus items in columns marked * refer to the extra cost through the combing pro- cess. The particulars of these are given on p. 239. The productions per spindle are given on p. 204. Costs of producing Yarns by Ring Spinning. — The cost of preparing the cotton up to the roving for ring spinning is greater than for mules. In the roving stage the cost is from 25 to 33 per cent, more on account of finer roving required. This necessitates more machinery for preparing the roving. The costs of labour in the spinning process, when producing the classes of yarn for which ring frames are most adapted, is in some cases as much as 50 per cent, less than in mule spinning process. Besides the extra preparation, a better class of cotton has to be used, and even then the yarn is not in a convenient form for transport when it leaves the spinning machine. The cost for winding the yarn in a convenient form for sale is consider- able. This latter item is dealt with in another part of this work. The following are the yarn and cotton quotations for June 29, 190G. These are given for comparison with the estimated costs contained on the foregoing pages. 236 COTTON SPINNING CALCULATIONS From the "Manchester Guardian," June 30, 1906. Good Bhow- nuggar. Per pound. 20^ water twist. Per pound. Middling American. Per pound. 32" cop twist. Per pound. Fully good fair Egypt. Per pound. 60' twist Egypt. Per pound. 1905. d. d. d. d. d. d. September 1 5 8i 5-83 S^ ^li 13| 8 4|i 8i 5-56 8i 7|i ISg „ 15 4ii 8i 5-50 8i 7|i 133 22 413 8i 5-64 8i 7}i 13i 29 4|i 8i 574 8i vii 13i October 6 4U 8J 5-41 8^ 7}^' 131 „ 13 ^W 8 5-32 8J 7}i 13J „ 20 ^W 8J 5-42 8J 7ii 13i ,, 27 m 8i 5-71 Si 8 131 November 3 4ii 8i 5-91 8i 81 131 10 4{i 8^ 616 8J Si • in 17 4}i 81 5-93 8| 81 14J 2i 4{i SI 611 9 81 14J December 1 4i m 616 81 81 141 8 5 9 6-42 9^ 8ft 14i 15 47 8? 6-29 % 81 14i „ 22 4}i 8f 6-31 9 81 141 29 H 8U 6-24 9 81 141 1906. January 5 Iji 81 6-23 9 8k 141 12 ^ 81 6-09 m 8tI 141 „ 19 4| 8i 6-30 »i 81 141 „ 26 4|i 8i 612 8f 8i 14i February 2 ^ 8i 5-99 8i 8?, 14| 9 45 8.1 5-87 8i 8\h 15J 16 ^ 8i 5-91 8i 81 15i 23 4| 8i 5-73 81 81 15i March 2 41 8,^B 5-78 8i 9V8 15i 9 ^ 8t*8 5-92 8| 9| 151 „ 16 ^ 8t^s 5-77 81 91 15i „ 23 n 8.1 5-84 81 9,'b 16^ „ 30 n 8i 6-03 8| 91 15i April 6 41i 81 6-10 9 91i 161 „ 12 4{i 8i 6-16 9| 101 i6i » 20 4U 81 604 9^ lOi 16i „ 27 4^ 8}^ 607 9J lOi 16i May 4 m 8? 608 9 101 16i „ 11 43 8| 6-18 9J 101 16i „ 18 4i 8Ji 6-25 % 101 i6i „ 25 43 8? 6-20 91 101 i«i June 1 4^4 8? 602 91 10| 16i » 8 41^ 8| 601 91 10| 16i „ 15 4|^ 8| 607 9i 101 16^ „ 22 ^ 8^ 612 n IOi'b 16^ „ 29 ^ 8:1 610 9i lOi 16J AND COSTS OF YAEN 237 From the "Cotton Factory Times," June 29, 1906. PRICE of medium tarns IN PENCE PER LB. Count. 4-16 10-28 20 30 32 36 34 40 50 60 70 80 AVeft. 8-9 013_Q 9 9i'6-9H 9^6-10 12|-13| 14-15 17H8i Twist in cop. gea^j. ^T6 ^'iS 9TV10i 9ft 12^ -lOi -llf -13i Bundle. 8F9i 9=1-10' lOJ-lll llM2i 1 Twofold. Bundle. Cop. — — 9H0i 9f'B-10^ loi-iii 10tV"t^b 11H2^ lli-12i Uf^li 13^131 — EGYPTIAN YARNS. 60 15A-1G^ — — 171-21 17i -20^ 70 16H7i — — — 19i-24 19I-23J 80 171 -18i — — — 21i-26f 211-26^ 90 18i-20i — — — 23^-30 23^29^ 100 20i-22J — 25H3i 25i-32i Cotton, Official Quotations. June 29, 1906. American G.o. 5-73 American. L.M. Md. 5-93 611 G.M. G-33 F.G.M. 6-43 M.F. 6-61 M.F. Fair. G.F. Pemain Ceara Paraiba Maceio 5-78 5-85 5-77 *o-79 618 6-23 615 *6-17 6-44 6-45 6-39 *6-39 Fair. Egyptian. G.F. F.G.F. Gd. Egyptian, brown . . Ditto, upper . . . . ! 8? 91 8}i lOi 9e *9i Egyptian, brown, fine, 11^. Ditto, upper, fine, *10. Egyptian quotations do not refer to Bamia or Upper Egypt cotton. Nominal. 238 COTTON SPINNING CALCULATIONS Tnd ian. F.F. G.F. F.G.F. Gd. F.G. Fine. Broach .... _ _ 5i 5U 5Vb Bhownuggar . . . — *4i *ik *4i *43 HI No. 1 Oomra . . . — *n *41 *4| *43 HI Bengal — m Q2S ^35 3§i ii. i^% Tinnivelly . . . — 5A K3 ^8 5^ — Bengal, Superfine, 4|. * Nominal. The Costs of Power available at the Machines, in a Spinning Mill. Basis : EDgine and all plant connected therewith to develop 1000 I.H.P. Engines, boilers, and economizers — Pumps and all the necessary connections — Shafting and rope-gearing — Keservoirs, land, buildings, and approaches at £15 per I.H.P. = ^£15,000. Piatio of above costs — (a) Engines, 35 per cent. (b) Boilers and economizers, 20 per cent. (c) Shafting and rope-gearing, 15 per cent. (d) Reservoirs, land, buildings, and approaches, 30 per cent. Woi'king Expenses ; — £ «. d. Depreciation and upkeep inclusive on (a), {b), (c), at 10 per cent, per annum 1050 Depreciation and upkeep on (fZ), at 2i per cent. ... 112 10 Interest at 4 per cent, per annum on (a), (b), (c), {d) . . 600 Stores at £0*25 per I.H.P. per annum 250 Coals : 2 lbs. per I.H.P. per hour, at 7s. Qd. per ton . . 1 47G Insurance (fire, accident), at 10s. per cent, on £12,000 . 60 Labour 400 3948 10 Cost per I.H.P. per hour in pence (50 X 55 working hours) — 3948-5 X 240 50 X 55 X 1000 The inclusive j)ower required in spinning mills, is about AND COSTS OF YARN 239 1 I.H.P. per 63 spinning spindles in mills containing all mule spmdles, and about 1 I.H.P. per 44 spinning spindles in mills contammg all ring spinning spindles. The power required to drive the various machines- Hopper cotton pullers and feeders . . 1 LHP. per machine Simple Creighton opener 2^ ylfW ; For each extra cylinder or beater 2 For each lap machine . . 2 Jb or automatic feeders . l T7I • • • • -^ J) ,, i^ or pneumatic cleaning trunks. 1^ Other types of openers as above. Scutchers, single with lap machine .31 Cards -^~ Sliver lap Q.g Eibbon lap I'O ' Comber, per combing head .... 01 Drawing frames, 5 dels, per .... 1 Slubbing frames, 45 spindles per . . 1 Intermediate frames, 60 spindles per . 1 '^ Eoving and ring frames, 80 spindles per 1 Mules, 110-120 spindles per .... 1 '| The Cost of Spaces in Spinning MiUs.-This works out at about 2s. per square yard per annum, inclusive of lighting and rates The Extra Cost when the Process of Combing is introduced.— The productive capacity of a machine of the Heilmann type, as made by the principal makers, ranges from 300 to 500 lbs. per machine of eight heads. In the following estimate moderate working conditions have been assumed, the production being taken at 400 lbs. per week of 551 hours per machine, and the waste extracted at 18 per cent. The quantity of cotton required for treatment would there- in , 400 X 100 fore be ^ — = 488 lbs. Assuming a wastage of 2^ per cent, between the combing and carding stages, the amount of carded cotton required per 400 lbs. of combed would be 500 lbs. If a loss of 5 per cent is 240 COTTON SPINNING CALCULATIONS allowed for in the card, then '^ — ^ - — = weight of cotton required in card laps, 527 lbs. And if 5 per cent, loss be allowed for in opening and scutch- ,, 527x100 ^^^,, , ,, . , ,^^„ mg, then, ~ = 555 lbs. of raw cotton required per 400 lbs. of combed cotton. When combing is not in vogue this amount would be less to the extent of .^. /400 X 100 X 100\ ^^. ,,. ,,, „ Assuming the production of the card 350 lbs. per week, the extra carding machinery per 400 lbs. of combed sliver would be— (500 - 400 = 100 lbs.) = ^^ Taking the productive capacity of a scutcher at 8000 lbs., and that of the opener at 16,000 lbs. per week, respectively, the loss being 2 and 3 per cent, respectively, then the extra scutching and opening machinery would be — 106 . 109 scutchmg,gQQQ; opening, jg^ The extra labour involved, upon the following basis, would cost as follows : — Cost of treating 16,000 lbs. of scutched cotton. Mixing, opening and scutching, wages inclusive, £3 15s. The cost, therefore, of treating the extra cotton required (106 lbs. scutcher lap) would be — 3-75 X 240 X 106 _ . q , 16000 ~ ^*^''- Therefore the extra cost on account of labour under this head would be — 5*9 Tjrx = 0"01475(7. per pounds of combed cotton AND COSTS OF YARN 241 Taking the labour in carding at 28s. per 14 cards inclusive, the cost per pound of combed sliver would be — —- — -^^ = 0*01701(?. per pound of combed sliver 350 X 14 X 400 ^ ^ The costs of labour involved in preparing the cotton for and in combing : One person, at 18s. per week, to attend the sliver and ribbon lap machines. Production, 2450 lbs. per week. — r— — -^^ — -~r— = 0108fL per pound of combed cotton 2450 X 400 ^ ^ One person, at 20s., per six combing machines inclusive of cost of overlooking — 20 X 12 n 77^ = O'l^^- per pound of combed sliver b X 400 ^ ^ Other expenses : Costs on account of the machinery — Approsimate Proportional cost coat. per combing machine. £ £ Cotton puller 140 0*92 Opener 300 1-97 Scutcher 180 2-36 Card 100 28-6 Silver lap 60 12-0 Kibbon lap 140 28-0 Comber 170 170*0 Total . . . £243-85 Eepair and upkeep at Ti per cent, per annum oii\ _ n-,Q o £243-85 ~ j - ^1«'289 Depreciation at 7i per cent, per annum on £243*85 = 18'289 Interest at 5 per cent, per annum on £243*85 . . = 12192 £48-770 Cost, under this head, per pound of "1 48-77 x 240 I = Z^\/\"r = 0-585^/. combed sliver j 50 X 400 242 COTTON SPINNING CALCULATIONS Extra stock of cotton in process through combing, say 400 lbs. per combing machine of 8 heads. Value of this at 8d per lb. = £13-3. Interest on £13'3 at 5 per cent, per annum = £0'665 Therefore cost per pound of combed sliver = --^ 77-^- = 0-008 ^ ^ 50 X 400 Extra cost on account of space, at 2s. per square yard per annum — Proportional area : square yards. Space per combing machine (400 lbs.), 15 square yards = 15-0 ribbon lap ,, (2450 lbs.), 15 „ = 2*5 sliver „ 12 „ =2-0 19-5 19"5 X 2 X 12 Cost per pound of combed sliver = — -7^ ,^^ = 0*0234f/. ^ '- 50 X 400 Extra cost on account of power, at 0"344(/. per I.H.P. per hour — Proportional power. Comber (400 lbs.) | I.H.P. 0-75 Eibbon lap machine (2450 lbs.) 1 ,, ^ Sliver „ ,, h „ f The extra cost on account of the waste extracted — Waste at the combing stage, 88 lbs. Extra waste at the previous stage, not returnable to mixing, 555 - 444 = 111 lbs. Therefore 111 + 400 = 511 lbs. the amount of raw cotton required per 400 lbs. combed, and therefore the cost of the cotton per pound at the combing head on this account is — Sd. X 511 400 = 10'22(^?. per pound AND COSTS OF YARN 24 Summary of Costs. Per pound of combed sliver. Labour : On account of extra mixing, opening, and scutching . 0'01475 carding 0-01715 „ Preparing the comber lap 0"108 „ Combing 0*1 Machinery and upkeep, repairs, and stores 0'585 Extra stock of cotton 0-008 Space 0-0234 Power 0-0473 Tlie total expenses nominally unaffected by changes in cotton values 0-9026 Value of the cotton at the combing head 10-22 11-1226 Cost of raw cotton 8-0 Extra cost of combing (value of the waste reserved) .... 3-1226 Allow for value of the waste I'O Nett extra cost of combing 2-1226 80^ — The cost of combing, when the raw cotton costs 11,^':/. per pound and the waste at this stage is 18 per cent., and 10 per cent, previous, allowing 50 per cent, of the cotton value for comber waste sold — 11"(/ Value of the waste = 18 per cent. 1 lb. at — ^' = 1'07(/. per pound The extra waste made in scutching and carding will be worth about 2.} per cent, of the cotton price per pound — The cost of the cotton at the combing head is therefore HZ X 100 72 = 16-4(?. The cost of spinning 80' uncombed on the basis of 19 hanks produced per spindle (see p. 235) — 244 COTTON SPINNING CALCULATIONS 1-72 X 80 _.,,., The other expenses of combing — 0-9026fL per pound Hence, assuming the waste made at the comber is sold at a price per pound equal to half the cost price of the raw cotton, then the extra cost of combing in this case would be — 18 per cent., 1 lb. x 'Tjd. = 0'T2d. The cost of combing = 11-1226 - B'O - 072 = 2-5026(/. per pound 11*1226 10-22 The expenses exclusive of the loss in waste .... 0"9026(Z. 10-22 8-0 The cost on account of the waste extracted, assuming it has no value 2*22 Costs of 80' combed as per tabulated data on p. 235. The cost of combing and spinning when the raw cotton costs llld. per pound. The cost of spinning (uncombed) as per tabulated data on p. 235— 1-72 X 80 _^- „ „ , — = 7 25 per lb. of yarn The cost of the cotton at the combing\ head, through waste loss, neglect-[= 16-4 ,, ,, ing value derived from sale ] The expenses of combing, excluding] aoaoa waste f- ^"^^^^ " " AND COSTS OF YAEN 245 Less the value of 18 per cent, waste) made in combing (at half price of = -1-07 per lb. of yarn. raw cotton per pound) I Less the value of waste made prior to ) combing (at 2^ per cent, on the = -0-295 raw cotton price) J " »» Cost per pound of yarn = 231876f?. Example of the method adopted in estimating the cost given below- Cardincj : 850 lbs. per card — Cost per pound Labour: 2s. lid per card, inchisive of over- .s. d. y'^"'"*!'""- looking and card head tenter 2 11 = 0-043-^ Power: 1 H.P. per card at 0-34rZ. per hour . 1 GT = O-Q-^-^O Machinery: £100 per card, 10 per cent, for loss, depreciation, and upkeep 4 1 = 0-057G Space : 10-58 square yards per card at 2s. per y^'"^ 5-18 =0-0061 8 11-88 0-1289 The cost at the drawing and subsequent stages is given per productive unit, on account of the wide range of variation in then- production. In order, therefore, to estimate the cost per pound, the production per delivery or per spindle is required. The production can be ascertained in the manner explained in other parts of this book. The Departmental Costs in Spinning Carded aualities of Yarn — In estimating these costs up-to-date conditions have been taken as the basis. The cost of space has been assessed at 2s. per square yard per annum, inclusive. But no allowance has been made for waste. Mixhuj-Cotton and W.ufe Stormje-Openh.g—ScutcU ruj- Cost in pence por pound T , of yarn spun. L'-ibonr ^,^^^ l^'^f. 0-0255 ^^^^^^'"^^•y 0-0144 ^"^^^^ 0-00317 0-07007 246 COTTON SPIKXIXG CALCULATIONS Carding — Cost in pence per card per week. Labour 35'0 Power 18-7 Machinery 49-0 Space 5'18 107-88 Drawing — Cost in pence per delivery per week. Labour 12'5 Power 3'75 Machinery 16-0 Space 0-7G 0. 9,. 01 Fly Frames : Sluhber — Cost in pence per spindle per week. Labour 3'25 Power 0-415 Machinery 0-87 Space 0-195 4-730 Intermediate — Labour 1-75 Power 0-31 Machinery 0-575 Space 01 2-735 Roving — Labour 0-88 Power 0-268 Machinery 0-4 Space . " 0-067 1-615 Mules — Labour 0-45 Power 0-156 Machinery 0-15 Space 0075 0-831 AND COSTS OF YARN 247 Rings — Cost in pence per ppindle per week. Labour 0*25 Power 0-235 Machinery 0-216 Space 0-029 0-730 Twining — Labour 0-66 Power 0-113 Machinery 0-12 Space 0-067 0-960 In twining the waste and costs of steaming and unpacking and packing the yarn must be added. The waste is sometimes a considerable addition to the cost. Twice the labour cost should always more than cover all expenses. Ring Doubling — Cost in pence per spindle per week. Labour 0-5 Power 0-312 Machinery 0-25 Space 0-044 1-106 Other expenses — namely, waste, travellers, grease, spindle banding, bobbins — are considerable. The "waste" should always be considered as a separate item ; 0*25 is a reasonable allowance for the rest. Doubling Winding, or Winding.— The production per spindle is considered good at 75 per cent, of the calculated without allowances. The number of spindles attended by one person may be estimated from the rate the winder can piece up as follows: Assume the winder can piece up at the average rate of 12 ends per minute, and that in the course of unwinding each ring bobbin end breaks twice, allowing 25 per cent, for the spindles stopped through incidental breakages. 248 COTTON SPINNING CALCULATIONS On this assumption the production per winder will be — 55 hrs. X 60 mins. x 12 x ounces contained on each bobbin 2 X 16 = pounds per winder Number of spindles per winder _ pounds per winder j_ ok ~ 75 per cent, calculated production per spindle ^ A Method of Ascertaining the Production of Reels. — The pro- duction of 40-hank reels in 55 hours when worked at 250 revolutions of the swift per minute, allowing two stops per bobbin unwound, and 5 seconds for each stop, the bobbins containing 0*75 oz. of counts 20^ the time lost in tying and doffing being 3 minutes. The time taken to fill the reel (40 hanks) if no stoppages 80 X 7 X 60 = ?r^rpr seconds ZoO The number of stops in filling the reel 840 0-75 ^ X 840 X 20 lb X 2 The time lost in filling the reel through stopping 840 ^ X 840 X 20 lb X 2 X 5 X 40 seconds The time taken to fill and doff, allowing two stoppages per bobbin unwound ^ 80 X 7 X 60 840x16x2x5 xJO 250 "^ 0-75x840x20 + ^^^ = 134-4 + 427 + 180 seconds = 12-37 minutes The production per week in pounds 55 X 60 , _„^ ,, AND COSTS OF YARN 249 The weekly earnings of winders and reelers vary from 14.s. to 24s. per week, and the cost per pound of yarn treated, varies, in this work, comparing districts, more than in any other section of the spinning mill. The numerous departmental wage lists and the difference in these, in the various districts, do not admit of the costs in wages being treated, in a work of this kind, in any other manner than that adopted. Although these lists differ on paper, competition has resulted in this difference in the costs— being that approaching the vanishing point, when reduced to a basis embodying quantity and quality of production. INDEX Attenuation. See Draft Backing-off and taking-in motion, 157, IGO, 178 Bale breakers or cotton pullers, 15-25 gearing in, 15, 21 hopper type of, 15, 21-25 Belt and rope driving, 12 Brooks and Shaw's type of differential (slubber frame), 138-140 Builder wheel in mule, 168 ascertaining suitable, in changing counts, 168 changes in, 168 in ring frame, 210 Building motion, 159, 178 Card calculations, 56 conditions controlling output of, G6 Carding department, proportions of machinery in, 141 parts, conditions respecting actions of, G(J functions of lickerin, cylinder, flats, doffer, 66-68 Combing machines, 84-101 detaching rollers, 87 drafts in, 89, 97 adjustment in, 99 lap rollers, 87 Nasmith and Heilmann ma- chines compared, 95 Nasmith's, gearing in, 84-8(5, 95-97 productive, 93 Cone drums, use of, in fly frames, 126 Constants for twist — normal, for roving, 111, 112 standards for single yarn, 161, 214 for folded yarn, 216 crochet, 217 fish netting, 217 knitting yarns and embroidery, and for mercerizing, 217 sewings, 217 Costs of yarn, 231-247 by mule spinning, 231 by ring spinning, 235 Cost of yarn extra when combing intro- duced, 239 departmental, 249 winding and reeling, 247, 248 of power available in mills, 288 of space in spinning mills, 209 Cotton, names applied to. in its prepara- tion, 71 system of counting, in its stages of preparation, 71 Cotton pullers or bale breakers, 15-25 gearing in, 15, 21 ■ hopper machine, 15, 21-25 Count, 71, 117 changes in, in mule, 157 ~ in ring frame, 209 of laps made by openers and scutchers, 52 — — changing, ascertaining suitable building wheel in, 168 of intermediate roving, 150 of sliver at the drawing frame, 151 of slubbing rove, 150 Counting cotton, system of, 71. See aho Count Curtis and Rhodes type of differential (roving frame), 129 Differentials, principal types of, 127-140 Brooks and Shaw's (slubber frame), 138-140 Curtis and Rhodes (roving frame), 129 Fallows motion (slubbing frame), 135 Tweedale (intermediate frame), 133 use of, in fly frames, 120 Dobson's ord. mule, 177 gearing in, 177, 195 double-speed and hastening motion, 190 Draft, 19, 35 between various parts, how ascer- tained, 62 how altered, 64, 65 changes in total, 69 in combing machines, 89, 97 252 INDEX Draft in drawing frames, 103, 107, 109 iu fl}- frames, 142, 151 i in mules, 157 in openers, 3i-40 ' in ribbon lap machines, 82 in ring frames, 209 in scutchers, 43-47 ] in shver lap machines, 78 Drawing frame, 102 calculations relating to, 103 coiling of sliver, spacing, 105 count of sliver at, 151 drafts, 103, 107, 109 effect of atmospheric changes, 102 system of gearing rollers, 108 rollers, analysis of action of, 152 functions of, 153 I)river and driven wheels, eflect of chaoging, 9, 10 Driving, rope and belt, 12 speeds and sizes of driving surfaces, 12-15 Equilibrium, state of, in yarn, 223 Fallows t\'pe of differential (slubbiug frame), 135 Fillet, length and preparation of, re- quired to cloth cylindrical surface, 75 Flats, in cards, functions of, 67 rate of movement of, 67 Fly frames, 110-152 ■ — consequences of altering value of cone train, 114 cone drums, use of, 126 count, 150, 151 changes in. 118 draft, 142,151 alterations in, 117, 118. 119 dififerentials, principal tvpes of, 127-140 use of, 12G drawing rollers, action of, analysis, 152 gearing in, 112-115 hank indicators, 154 " preparations," 141 ■ processes, three stages, 141 ■ production in, 145 rate of winding and spacing of coils, 120 speed of spindles, 149 speeds, 115, 140 twist constants, 111 twisting in, object of. Ill winding in, obtained bv bob- bin, 125 Gain, or drag, 161, 164 changes, 166, 186 Gearing iu bale breakers, 15, 21 in carding machines, 56 in Dobson's double-speed and hastening motion, 190 in draw frames, 103 in fly frames, 112 in mules, 156 — — Dobson and Barlow's, 177, 195 Piatt's, 183, 191, 192 various trains, 162, 177-190 in Nasmith combing machine, 84 iu openers, 25 in Piatt's knocking-off motion, 51 in ribbon lap machines, SO in ring frames, 204 doubling frames, 224 rollers, 108 in scutchers, 41 in sliver lap machines, 76 in twiner mule, 228 various trains of, calculations and other particulars of. 161-177 Half-lap, 75 preparing, 75 Hank indicators, 154, 200-203 Hastening motion, 161 Dobson's, 190 Hetherington mule, 162 Hopper type of cotton puller, 21-25 gearing in, 21 usefulness of, 24 Hunting cog measuring or length motion, used in openers and scutchers. 48 advantage of, 50 Indicators, hank, for frames and mules, 158,200-203 length, 200 speed, their use, 198 Jacking or ratching motion, 158. 162 Piatt's, 191 t Trelfall'e, 193 ' Knocking-off motion in scutchers, Piatt's, I ^^ Laps, 71 i changes in weight and count of, made by openers and scutchers, 52 ' length of, 49-51 rollers, 87 Length and hank indicators, 200-203 1 stop motion, 150 INDEX 253 Motiou, rate of, calculating, when tooth- gear employed, 1 transmission of, 1-15 Motions — backiug-oflf and takini'-in, 157, 1(J0 178 building, 159, 178 double-speed, 159, 19U hastening, 161, 190 jacking or ratching, 158, 162, 191, 193 knocking-off, 51 length stop or full bobbin, 156 receding, 158, 178 roller delivery, 160 twisting, 159 Movement of tooth wheels, direction of, Mules, 156-204 calculations, 156, 183 compared with ring frame, 213 costs of yarn, 231 counts, changes in, 157 drafts in, 157 Dobson's and Barlow's, 177,190, 194 gearing in, 150 various trains of, 162-167 Hetheriugton, 162 losses in driving in, 194, 196 motions, 157-161 Piatt's, 183, 191, 192 productions in, 204 proportion of machinery forming a "preparation," 142 Trelfall's, 193 twiner, 228-230 twist per inch, 197 wheel train values in, conditions governing changes in, 161 various, and range in size of wheels, 177-190 Openers, 15-40, 48-56 changes in weight and count of laps made by, 52 drafts in, 34-40 gearing in, 25 hunting cog measuring or length motion used in, 48 productions, speeds, and controlling factors, 54 Overscutching, 55 Piatt, Bros., jacking motion, 191 Piatt's knocking-off motion, 51 ■ gearing in, 51 Plucking from feed rollers, 54 "Preparation," 70, 141 proportion of machinery forming a, in mule spinning and ring frame spinning, 142 Productions, and their controllintr fac tors, 53, 54 Keceding motion, 158, 178 Revolution of wheels, law, 1 Ribbon lap machines, 80 drafts in, 82 — ; production in, 83 Ring doubling frames, 224-228 gearing in, 224 production in, 226 slippage in, 228 twist obtained, 224 ■ winding, 247 Ring frames, 204-224 builder wheel (ratchet), 210 compared with mule, 213 costs of yarn, 235 counts, changing, 209 gearing in, 204 looses in driving spindles, 212 productions in, 213 proportion of machinery form- ing a " preparation " in, 142 speeds of spindles, 206, 212 twist per inch, 207 Ring spinning. See Ring frames Roller delivery motion, 160 Rope and belt driving, 12 calculating speeds and sizes of driving surfaces, 12-15 Rotation, direction of, 6 of wheels in any direct train, rela- tive rates of, law, 3 Scutchers, 41-56 changes in weight and count of laps made by, 52 draft in, 43-47 gearing in, 41-43 hunting cog measuring or length motion used in, 48 ^ particulars of driving, 41 productions, speeds, and controlling factors, 54 Sliver, or web, 65, 71 coiling of, 105 ■;;-;— weight of the card, 152 Sliver lap machines, 76 drafts in, 78 production in, 79 • to alter, 79 Speed indicators, 198 Speeds in scutchers and their control- ling factors, 53, 54 altering, 61 Stop motions, length. 156 254 INDEX Tachometer, the, 198, 199 Tooth-gear, calculatiug rale of motion wlien, employed, 1 wheels, direction of movement of, 2 Transmission of motion, 1-15 Trelfall's jacking motion, 19:> Tweedale type of differential (later- mediate frame), 133 Twiner mule, 228-230 gearing in, 228 Twist, constants, for roving, normal, 111, 112 standards for single yarns, 161,214 ■ doubling, aims and effects of, 220 constants used in, 216 in roving direction and usefulness, 111 effects of. 211 in single yarns. 21.3 influence of direction of, in folded yarns, 218 object of, 111, 2U1 obtained in ring doubling frames, 224 per inch and per draw, 197 in ring frames, 207 relative resistance of yams to, 222 ■ standards, for folded yarns, 216 for 6in,(,'le yarns, 214 state of equilibrium, 223 influence ou breaking strength, 215, 216 twisting two or more threads together, 219 Wheel trains, 4-11 calculating value of, 8 direct and indirect, 4-6 effects of changing wheels, 9 values of, in mules, conditions governing changes in, 161 various, particulars of, 177 See Gearing Wheels, classification of : driver, driven, carrier, 6 direction of rotation, 6 effects of changing, 9 law of revolution, 1 relative rates of rotation, 3 Winding in fly frames, how obtained, 125 Wrapping, 70 Yarn, 71 costs of (q.v.), 231-247 doubling, aims and effects of, 220 folded, twist standards for, 216 influence of direction of twist on strength of, 218 relative resistance of, to twist, 222 singli', twist standards for, 214 . effects of twist in, 214, 215 state of equilibrium, 223 t'ltal length of. per draw, 197, 2J3 testing for breaking strength, 215, 216 ».©• THE END '^B ~ "»- FSIKTED Br WILLIAM CLOWES ASD SOKS, LIMITED, LOKDOX AKD BECCLES. 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